User:RazrRekr201/Table of constants
Table of constants and other irrational or transcendental numbers
[edit]Value | Name | Graphics | Symbol | LaTeX | Formula | Nº | OEIS | Continued fraction | Year | Web format |
---|---|---|---|---|---|---|---|---|---|---|
0,70444 22009 99165 59273 | Carefree constant 2 [1] | N[prod[n=1 to ∞] {1 - 1/(prime(n)* (prime(n) 1))}] |
OEIS: A065463 | [0;1,2,2,1,1,1,1,4,2,1,1,3,703,2,1,1,1,3,5,1,...] | 0.70444220099916559273660335032663721 | |||||
1.84775 90650 22573 51225 [Mw 1] | Connective constant [2][3] |
as a root of the polynomial |
sqrt(2 sqrt(2)) | A | OEIS: A179260 | [1;1,5,1,1,3,6,1,3,3,10,10,1,1,1,5,2,3,1,1,3,...] | 1.84775906502257351225636637879357657 | |||
0.30366 30028 98732 65859 [Mw 2] | Gauss-Kuzmin-Wirsing constant [4] |
where is an analytic function with . |
OEIS: A038517 | [0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1,...] | 1973 | 0.30366300289873265859744812190155623 | ||||
1,57079 63267 94896 61923 [Mw 3] | Favard constant K1 Wallis product [5] |
Prod[n=1 to ∞] {(4n^2)/(4n^2-1)} |
T | OEIS: A069196 | [1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...] | 1655 | 1.57079632679489661923132169163975144 | |||
1,60669 51524 15291 76378 [Mw 4] | Erdős–Borwein constant[6][7] | sum[n=1 to ∞] {1/(2^n-1)} |
I | OEIS: A065442 | [1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...] | 1949 | 1.60669515241529176378330152319092458 | |||
1.61803 39887 49894 84820 [Mw 5] | Phi, Golden ratio [8] | (1 5^(1/2))/2 | A | OEIS: A001622 | [0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...] = [0;1,...] |
-300 ~ | 1.61803398874989484820458633436563812 | |||
1.64493 40668 48226 43647 [Mw 6] | Riemann Function Zeta(2) | Sum[n=1 to ∞] {1/n^2} |
T | OEIS: A013661 | [1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...] | 1826 to 1866 |
1.64493406684822643647241516664602519 | |||
1.73205 08075 68877 29352 [Mw 7] | Theodorus constant[9] | (3(3(3(3(3(3(3) ^1/3)^1/3)^1/3) ^1/3)^1/3)^1/3) ^1/3 ... |
A | OEIS: A002194 | [1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...] = [1;1,2,...] |
-465 to -398 |
1.73205080756887729352744634150587237 | |||
1.75793 27566 18004 53270 [Mw 8] | Kasner number | Fold[Sqrt[#1 #2] &,0,Reverse [Range[20]]] |
OEIS: A072449 | [1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...] | 1878 a 1955 |
1.75793275661800453270881963821813852 | ||||
2.29558 71493 92638 07403 [Mw 9] | Universal parabolic constant [10] | ln(1 sqrt 2) sqrt 2 | T | OEIS: A103710 | [2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,7,2,1,...] | 2.29558714939263807403429804918949038 | ||||
1.78657 64593 65922 46345 [Mw 10] | Silverman constant[11] | |
Sum[n=1 to ∞] {1/[EulerPhi(n) DivisorSigma(1,n)]} |
OEIS: A093827 | [1;1,3,1,2,5,1,65,11,2,1,2,13,1,4,1,1,1,2,5,4,...] | 1.78657645936592246345859047554131575 | ||||
2.59807 62113 53315 94029 [Mw 11] | Area of the regular hexagon with side equal to 1 [12] | 3 sqrt(3)/2 | A | OEIS: A104956 | [2;1,1,2,20,2,1,1,4,1,1,2,20,2,1,1,4,1,1,2,20,...] [2;1,1,2,20,2,1,1,4] |
2.59807621135331863029116951225880855 | ||||
0.66131 70494 69622 33528 [Mw 12] | Feller-Tornier constant [13] |
[prod[n=1 to ∞] {1-2/prime(n)^2}] /2 1/2 |
T ? | OEIS: A065493 | [0;1,1,1,20,9,1,2,5,1,2,3,2,3,38,8,1,16,2,2,...] | 1932 | 0.66131704946962233528976584627411853 | |||
1.46099 84862 06318 35815 [Mw 13] | Baxter's Four-coloring constant [14] |
Mapamundi Four-Coloring |
|
3×Gamma(1/3) ^3/(4 pi^2) |
OEIS: A224273 | [1;2,5,1,10,8,1,12,3,1,5,3,5,8,2,1,23,1,2,161,...] | 1970 | 1.46099848620631835815887311784605969 | ||
1.92756 19754 82925 30426 [Mw 14] | Tetranacci constant | Positive root of | Root[x x^-4-2=0] | OEIS: A086088 | [1;1,12,1,4,7,1,21,1,2,1,4,6,1,10,1,2,2,1,7,1,...] | 1.92756197548292530426190586173662216 | ||||
1.00743 47568 84279 37609 [Mw 15] | DeVicci's tesseract constant | The largest cube that can pass through in an 4D hypercube.
Positive root of |
Root[4*x^8-28*x^6 -7*x^4 16*x^2 16 =0] |
A | OEIS: A243309 | [1;134,1,1,73,3,1,5,2,1,6,3,11,4,1,5,5,1,1,48,...] | 1.00743475688427937609825359523109914 | |||
1.70521 11401 05367 76428 [Mw 16] | Niven's constant [15] | 1 Sum[n=2 to ∞] {1-(1/Zeta(n))} |
OEIS: A033150 | [1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,...] | 1969 | 1.70521114010536776428855145343450816 | ||||
0.60459 97880 78072 61686 [Mw 17] | Relationship among the area of an equilateral triangle and the inscribed circle. | Sum[1/(n Binomial[2 n, n]) , {n, 1, ∞}] |
T | OEIS: A073010 | [0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6,...] | 0.60459978807807261686469275254738524 | ||||
1.15470 05383 79251 52901 [Mw 18] | Hermite Constant [16] | 2/sqrt(3) | A | 1 OEIS: A246724 |
[1;6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] [1;6,2] |
1.15470053837925152901829756100391491 | ||||
0.41245 40336 40107 59778 [Mw 19] | Prouhet–Thue–Morse constant [17] | where is the Thue–Morse sequence and Where |
T | OEIS: A014571 | [0;2,2,2,1,4,3,5,2,1,4,2,1,5,44,1,4,1,2,4,1,1,...] | 0.41245403364010759778336136825845528 | ||||
0.58057 75582 04892 40229 [Mw 20] | Pell Constant [18] | N[1-prod[n=0 to ∞] {1-1/(2^(2n 1)}] |
T ? | OEIS: A141848 | [0;1,1,2,1,1,1,1,14,1,3,1,1,6,9,18,7,1,27,1,1,...] | 0.58057755820489240229004389229702574 | ||||
0.66274 34193 49181 58097 [Mw 21] | Laplace limit [19] | (x e^sqrt(x^2 1)) /(sqrt(x^2 1) 1) = 1 |
OEIS: A033259 | [0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601,...] | 1782 ~ | 0.66274341934918158097474209710925290 | ||||
0.17150 04931 41536 06586 [Mw 22] | Hall-Montgomery Constant [20] | 1 Pi^2/6 2*PolyLog[2, -Sqrt[E]] | OEIS: A143301 | [0;5,1,4,1,10,1,1,11,18,1,2,19,14,1,51,1,2,1,...] | 0.17150049314153606586043997155521210 | |||||
1.55138 75245 48320 39226 [Mw 23] | Calabi triangle constant [21] | FindRoot[ 2x^3-2x^2-3x 2 ==0, {x, 1.5}, WorkingPrecision->40] |
A | OEIS: A046095 | [1;1,1,4,2,1,2,1,5,2,1,3,1,1,390,1,1,2,11,6,2,...] | 1946 ~ | 1.55138752454832039226195251026462381 | |||
1.22541 67024 65177 64512 [Mw 24] | Gamma(3/4) [22] | (-1 3/4)! | OEIS: A068465 | [1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,8,3,...] | 1.22541670246517764512909830336289053 | |||||
1.20205 69031 59863 28539 [Mw 25] | Apéry's constant [23] |
|
Sum[n=1 to ∞] {1/n^3} |
I | OEIS: A010774 | [1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11,...] | 1979 | 1.20205690315986328539973816151144999 | ||
0.91596 58631 77219 01505 [Mw 26] | Catalan's constant[24][25][26] | Sum[n=0 to ∞] {(-1)^n/(2n 1)^2} |
T | OEIS: A006752 | [0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,...] | 1864 | 0.91596586317721901505460351493238411 | |||
0.78539 81633 97448 30961 [Mw 27] | Beta(1) [27] | Sum[n=0 to ∞] {(-1)^n/(2n 1)} |
T | OEIS: A003881 | [0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...] | 1805 to 1859 |
0.78539816339744830961566084581987572 | |||
0.00131 76411 54853 17810 [Mw 28] | Heath-Brown–Moroz constant[28] | N[prod[n=1 to ∞] {((1-1/prime(n))^7) *(1 (7*prime(n) 1) /(prime(n)^2))}] |
T ? | OEIS: A118228 | [0,0,1,3,1,7,6,4,1,1,5,4,8,5,3,1,7,8,1,0,9,8,1,...] | 0.00131764115485317810981735232251358 | ||||
0.56755 51633 06957 82538 | Module of Infinite Tetration of i |
Mod(i^i^i^...) | OEIS: A212479 | [0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...] | 0.56755516330695782538461314419245334 | |||||
0.78343 05107 12134 40705 [Mw 29] | Sophomore's dream 1 J.Bernoulli [29] | Sum[n=1 to ∞] {-(-1)^n /n^n} |
OEIS: A083648 | [0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,...] | 1697 | 0.78343051071213440705926438652697546 | ||||
1.29128 59970 62663 54040 [Mw 30] | Sophomore's dream 2 J.Bernoulli [30] | Sum[n=1 to ∞] {1/(n^n)} |
OEIS: A073009 | [1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4,...] | 1697 | 1.29128599706266354040728259059560054 | ||||
0.70523 01717 91800 96514 [Mw 31] | Primorial constant Sum of the product of inverse of primes [31] |
Sum[k=1 to ∞] (prod[n=1 to k] {1/prime(n)}) |
OEIS: A064648 | [0;1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,...] | 0.70523017179180096514743168288824851 | |||||
0.14758 36176 50433 27417 [Mw 32] | Plouffe's gamma constant [32] | Arctan(1/2)/pi | T | OEIS: A086203 | [0;6,1,3,2,5,1,6,5,3,1,1,2,1,1,2,3,1,2,3,2,2,...] | 0.14758361765043327417540107622474052 | ||||
0.15915 49430 91895 33576 [Mw 33] | Plouffe's A constant [33] | 1/(2 pi) | T | OEIS: A086201 | [0;6,3,1,1,7,2,146,3,6,1,1,2,7,5,5,1,4,1,2,42,...] | 0.15915494309189533576888376337251436 | ||||
0.29156 09040 30818 78013 [Mw 34] | Dimer constant 2D, Domino tiling[34][35] |
C=Catalan |
N[int[-pi to pi] {arccosh(sqrt( cos(t) 3)/sqrt(2)) /(4*Pi)dt}] |
OEIS: A143233 | [0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...] | 0.29156090403081878013838445646839491 | ||||
0.49801 56681 18356 04271 0.15494 98283 01810 68512 i |
Factorial(i)[36] | Integral_0^∞ t^i/e^t dt |
C | OEIS: A212877 OEIS: A212878 |
[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...] - [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] i |
0.49801566811835604271369111746219809 - 0.15494982830181068512495513048388 i | ||||
2.09455 14815 42326 59148 [Mw 35] | Wallis Constant | (((45-sqrt(1929)) /18))^(1/3) (((45 sqrt(1929)) /18))^(1/3) |
T | OEIS: A007493 | [2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4,...] | 1616 to 1703 |
2.09455148154232659148238654057930296 | |||
0.72364 84022 98200 00940 [Mw 36] | Sarnak constant | N[prod[k=2 to ∞] {1-(prime(k) 2) /(prime(k)^3)}] |
T ? | OEIS: A065476 | [0;1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,8,2,1,1,...] | 0.72364840229820000940884914980912759 | ||||
0.63212 05588 28557 67840 [Mw 37] | Time constant [37] |
|
lim_(n->∞) (1- !n/n!) !n=subfactorial |
T | OEIS: A068996 | [0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [0;1,1,1,2n], n∈ℕ |
0.63212055882855767840447622983853913 | |||
1.04633 50667 70503 18098 | Minkowski-Siegel mass constant [38] | N[prod[n=1 to ∞] n! /(sqrt(2*Pi*n) *(n/e)^n *(1 1/n) ^(1/12))] |
OEIS: A213080 | [1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..] | 1867 1885 1935 |
1.04633506677050318098095065697776037 | ||||
5.24411 51085 84239 62092 [Mw 38] | Lemniscate Constant [39] | Gamma[ 1/4 ]^2 /Sqrt[ 2 Pi ] |
OEIS: A064853 | [5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2,...] | 1718 | 5.24411510858423962092967917978223883 | ||||
0.66170 71822 67176 23515 [Mw 39] | Robbins constant [40] | (4 17*2^(1/2)-6 *3^(1/2) 21*ln(1 2^(1/2)) 42*ln(2 3^(1/2))-7*Pi)/105 |
OEIS: A073012 | [0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1,4,...] | 1978 | 0.66170718226717623515583113324841358 | ||||
1.30357 72690 34296 39125 [Mw 40] | Conway constant [41] | A | OEIS: A014715 | [1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1,...] | 1987 | 1.30357726903429639125709911215255189 | ||||
1.18656 91104 15625 45282 [Mw 41] | Khinchin–Lévy constant[42] | pi^2 /(12 ln 2) | OEIS: A100199 | [1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9,...] | 1935 | 1.18656911041562545282172297863723712 | ||||
0.83564 88482 64721 05333 | Baker constant [43] | Sum[n=0 to ∞] {((-1)^(n))/(3n 1)} |
OEIS: A113476 | [0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3,...] | 0.83564884826472105333710345970011076 | |||||
23.10344 79094 20541 6160 [Mw 42] | Kempner Serie(0) [44] |
|
1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/11 1/12 1/13 1/14 1/15 ... |
OEIS: A082839 | [23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1,...] | 23.1034479094205416160340540433255981 | ||||
0.98943 12738 31146 95174 [Mw 43] | Lebesgue constant [45] | 4/pi^2*[(2 Sum[k=1 to ∞] {ln(k)/(4*k^2-1)}) -poligamma(1/2)] |
OEIS: A243277 | [0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5,...] | ? | 0.98943127383114695174164880901886671 | ||||
0.19452 80494 65325 11361 [Mw 44] | 2nd du Bois-Reymond constant [46] | (e^2-7)/2 | T | OEIS: A062546 | [0;5,7,9,11,13,15,17,19,21,23,25,27,29,31,...] = [0;2p 3], p∈ℕ |
0.19452804946532511361521373028750390 | ||||
0.78853 05659 11508 96106 [Mw 45] | Lüroth constant[47] | Sum[n=2 to ∞] log(n/(n-1))/n |
OEIS: A085361 | [0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16,...] | 0.78853056591150896106027632216944432 | |||||
1.18745 23511 26501 05459 [Mw 46] | Foias constant α [48] |
Foias constant is the unique real number such that if x1 = α then the sequence diverges to ∞. When x1 = α, |
OEIS: A085848 | [1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2,...] | 2000 | 1.18745235112650105459548015839651935 | ||||
2.29316 62874 11861 03150 [Mw 47] | Foias constant β | x^(x 1) = (x 1)^x |
OEIS: A085846 | [2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1,...] | 2000 | 2.29316628741186103150802829125080586 | ||||
0.82246 70334 24113 21823 [Mw 48] | Nielsen-Ramanujan constant [49] | Sum[n=1 to ∞] {((-1)^(n 1))/n^2} |
T | OEIS: A072691 | [0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...] | 1909 | 0.82246703342411321823620758332301259 | |||
0.69314 71805 59945 30941 [Mw 49] | Natural logarithm of 2 [50] | Sum[n=1 to ∞] {(-1)^(n 1)/n} |
T | OEIS: A002162 | [0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,1,1,1,2,1,1,...] | 1550 to 1617 |
0.69314718055994530941723212145817657 | |||
0.47494 93799 87920 65033 [Mw 50] | Weierstrass constant [51] | (E^(Pi/8) Sqrt[Pi]) /(4 2^(3/4) (1/4)!^2) |
OEIS: A094692 | [0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...] | 1872 ? | 0.47494937998792065033250463632798297 | ||||
0.57721 56649 01532 86060 [Mw 51] | Euler-Mascheroni constant |
|
sum[n=1 to ∞] |sum[k=0 to ∞] {((-1)^k)/(2^n k)} |
OEIS: A001620 | [0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...] | 1735 | 0.57721566490153286060651209008240243 | |||
1.38135 64445 18497 79337 | Beta, Kneser-Mahler polynomial constant[52] | e^((PolyGamma(1,4/3) - PolyGamma(1,2/3) 9)/(4*sqrt(3)*Pi)) |
OEIS: A242710 | [1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1,...] | 1963 | 1.38135644451849779337146695685062412 | ||||
1.35845 62741 82988 43520 [Mw 52] | Golden Spiral | GoldenRatio^(2/pi) | OEIS: A212224 | [1;2,1,3,1,3,10,8,1,1,8,1,15,6,1,3,1,1,2,3,1,1,...] | 1.35845627418298843520618060050187945 | |||||
0.57595 99688 92945 43964 [Mw 53] | Stephens constant [53] | Prod[n=1 to ∞] {1-hprime(n) /(hprime(n)^3-1)} |
T ? | OEIS: A065478 | [0;1,1,2,1,3,1,3,1,2,1,77,2,1,1,10,2,1,1,1,7,...] | ? | 0.57595996889294543964316337549249669 | |||
0.73908 51332 15160 64165 [Mw 54] | Dottie number [54] | cos(c)=c | OEIS: A003957 | [0;1,2,1,4,1,40,1,9,4,2,1,15,2,12,1,21,1,17,...] | ? | 0.73908513321516064165531208767387340 | ||||
0.67823 44919 17391 97803 [Mw 55] | Taniguchi constant [55] |
|
Prod[n=1 to ∞] {1 -3/ithprime(n)^3 2/ithprime(n)^4 1/ithprime(n)^5 -1/ithprime(n)^6} |
T ? | OEIS: A175639 | [0;1,2,9,3,1,2,9,11,1,13,2,15,1,1,1,2,4,1,1,1,...] | ? | 0.67823449191739197803553827948289481 | ||
1.85407 46773 01371 91843 [Mw 56] | Gauss' Lemniscate constant[56] |
|
pi^(3/2)/(2 Gamma(3/4)^2) | OEIS: A093341 | [1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1,...] | 1.85407467730137191843385034719526005 | ||||
1.75874 36279 51184 82469 | Infinite product constant, with Alladi-Grinstead [57] | Prod[n=2 to inf] {(1 1/n)^(1/n)} | OEIS: A242623 | [1;1,3,6,1,8,1,4,3,1,4,1,1,1,6,5,2,40,1,387,2,...] | 1977 | 1.75874362795118482469989684865589317 | ||||
1.86002 50792 21190 30718 | Spiral of Theodorus [58] | Sum[n=1 to ∞] {1/(n^(3/2) n^(1/2))} |
OEIS: A226317 | [1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19,...] | -460 to -399 |
1.86002507922119030718069591571714332 | ||||
2.79128 78474 77920 00329 | Nested radical S5 |
|
(sqrt(21) 1)/2 | A | A222134 | [2;1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,...] [2;1,3] |
? | 2.79128784747792000329402359686400424 | ||
0.70710 67811 86547 52440 0.70710 67811 86547 524 i [Mw 57] |
Square root of i [59] | (1 i)/(sqrt 2) | C A | OEIS: A010503 | [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] = [0;1,2,...] [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] i = [0;1,2,...] i |
? | 0.70710678118654752440084436210484903 0.70710678118654752440084436210484 i | |||
0.80939 40205 40639 13071 [Mw 58] | Alladi–Grinstead constant [60] | e^{(sum[k=2 to ∞] |sum[n=1 to ∞] {1/(n k^(n 1))})-1} |
OEIS: A085291 | [0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22,...] | 1977 | 0.80939402054063913071793188086309131 | ||||
2.58498 17595 79253 21706 [Mw 59] | Sierpiński's constant [61] |
|
-Pi Log[Pi] 2 Pi EulerGamma 4 Pi Log [Gamma[3/4]] |
OEIS: A062089 | [2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1,...] | 1907 | 2.58498175957925321706589358738317116 | |||
1.73245 47146 00633 47358 [Ow 1] | Reciprocal of the Euler–Mascheroni constant | 1/Integrate_ {x=0 to 1} -log(log(1/x)) |
OEIS: A098907 | [1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...] | 1.73245471460063347358302531586082968 | |||||
1.43599 11241 76917 43235 [Mw 60] | Lebesgue constant (interpolation) [62][63] | 1/3 2*sqrt(3)/pi | T | OEIS: A226654 | [1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1,...] | 1902 ~ | 1.43599112417691743235598632995927221 | |||
3.24697 96037 17467 06105 [Mw 61] | Silver root Tutte–Beraha constant [64] |
2 2 cos(2Pi/7) | A | OEIS: A116425 | [3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...] | 3.24697960371746706105000976800847962 | ||||
1.94359 64368 20759 20505 [Mw 62] | Euler Totient constant [65][66] |
zeta(2)*zeta(3) /zeta(6) |
OEIS: A082695 | [1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32,...] | 1750 | 1.94359643682075920505707036257476343 | ||||
1.49534 87812 21220 54191 | Fourth root of five [67] | (5(5(5(5(5(5(5) ^1/5)^1/5)^1/5) ^1/5)^1/5)^1/5) ^1/5 ... |
I | OEIS: A011003 | [1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2,...] | 1.49534878122122054191189899414091339 | ||||
0.87228 40410 65627 97617 [Mw 63] | Area of Ford circle [68] | pi Zeta(3) /(4 Zeta(4)) | [0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3,...] | 0.87228404106562797617519753217122587 | ||||||
1.08232 32337 11138 19151 [Mw 64] | Zeta(4) [69] | Sum[n=1 to ∞] {1/n^4} |
T | OEIS: A013662 | [1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,23,...] | ? | 1.08232323371113819151600369654116790 | |||
1.56155 28128 08830 27491 | Triangular root of 2.[70] |
|
(sqrt(17)-1)/2 | A | OEIS: A222133 | [1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,...] [1;1,1,3] |
1.56155281280883027491070492798703851 | |||
9.86960 44010 89358 61883 | Pi Squared | 6 Sum[n=1 to ∞] {1/n^2} |
T | A002388 | [9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,1,3,...] | 9.86960440108935861883449099987615114 | ||||
1.32471 79572 44746 02596 [Mw 65] | Plastic number [71] | (1 (1 (1 (1 (1 (1 )^(1/3))^(1/3))^(1/3)) ^(1/3))^(1/3))^(1/3) |
A | OEIS: A060006 | [1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,2,...] | 1929 | 1.32471795724474602596090885447809734 | |||
2.37313 82208 31250 90564 | Lévy 2 constant [72] | Pi^(2)/(6*ln(2)) | T | OEIS: A174606 | [2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...] | 1936 | 2.37313822083125090564344595189447424 | |||
0.85073 61882 01867 26036 [Mw 66] | Regular paperfolding sequence [73][74] | N[Sum[n=0 to ∞] {8^2^n/(2^2^ (n 2)-1)},37] |
OEIS: A143347 | [0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6,...] | 0.85073618820186726036779776053206660 | |||||
1.15636 26843 32269 71685 [Mw 67] | Cubic recurrence constant [75][76] | prod[n=1 to ∞] {n ^(1/3)^n} |
OEIS: A123852 | [1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33,...] | 1.15636268433226971685337032288736935 | |||||
1.26185 95071 42914 87419 [Mw 68] | Fractal dimension of the Koch snowflake [77] | log(4)/log(3) | I | A100831 | [1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7,...] | 1.26185950714291487419905422868552171 | ||||
6.58088 59910 17920 97085 | Froda constant[78] | 2^e | [6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...] | 6.58088599101792097085154240388648649 | ||||||
0.26149 72128 47642 78375 [Mw 69] | Meissel-Mertens constant [79] | gamma Sum[n=1 to ∞] {ln(1-1/prime(n)) 1/prime(n)} |
T ? | OEIS: A077761 | [0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296,...] | 1866 & 1873 |
0.26149721284764278375542683860869585 | |||
4.81047 73809 65351 65547 | John constant [80] | e^(π/2) | T | OEIS: A042972 | [4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,2,...] | 4.81047738096535165547303566670383313 | ||||
-0.5 ± 0.86602 54037 84438 64676 i |
Cube Root of 1 [81] | 1, E^(2i pi/3), E^(-2i pi/3) |
C | OEIS: A010527 | - [0,5] ± [0;1,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] i - [0,5] ± [0; 1, 6, 2] i |
- 0.5 ± 0.8660254037844386467637231707529 i | ||||
0.11000 10000 00000 00000 0001 [Mw 70] | Liouville number [82] | Sum[n=1 to ∞] {10^(-n!)} |
T | OEIS: A012245 | [1;9,1,999,10,9999999999999,1,9,999,1,9] | 0.11000100000000000000000100... | ||||
0.06598 80358 45312 53707 [Mw 71] | Lower limit of Tetration [83] | 1/(e^e) | OEIS: A073230 | [0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...] | 0.06598803584531253707679018759684642 | |||||
1.83928 67552 14161 13255 | Tribonacci constant[84] | (1/3)*(1 (19 3 *sqrt(33))^(1/3) (19-3 *sqrt(33))^(1/3)) |
A | OEIS: A058265 | [1;1,5,4,2,305,1,8,2,1,4,6,14,3,1,13,5,1,7,...] | 1.83928675521416113255185256465328660 | ||||
0.36651 29205 81664 32701 | Median of the Gumbel distribution [85] | -ln(ln(2)) | A074785 | [0;2,1,2,1,2,6,1,6,6,2,2,2,1,12,1,8,1,1,3,1,...] | 0.36651292058166432701243915823266947 | |||||
36.46215 96072 07911 7709 | Pi^pi [86] | pi^pi | OEIS: A073233 | [36;2,6,9,2,1,2,5,1,1,6,2,1,291,1,38,50,1,2,...] | 36.4621596072079117709908260226921236 | |||||
0.53964 54911 90413 18711 | Ioachimescu constant [87] | γ N[ sum[n=1 to ∞] {((-1)^(2n) gamma_n) /(2^n n!)}] |
2- OEIS: A059750 |
[0;1,1,5,1,4,6,1,1,2,6,1,1,2,1,1,1,37,3,2,1,...] | 0.53964549119041318711050084748470198 | |||||
15.15426 22414 79264 1897 [Mw 72] | Exponential reiterated constant [88] | Sum[n=0 to ∞] {(e^n)/n!} |
OEIS: A073226 | [15;6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7,...] | 15.1542622414792641897604302726299119 | |||||
0.64624 54398 94813 30426 [Mw 73] | Masser–Gramain constant [89] |
|
Pi/4*(2*Gamma 2*Log[2] 3*Log[Pi]- 4 Log[Gamma[1/4]]) |
OEIS: A086057 | [0;1,1,1,4,1,3,2,3,9,1,33,1,4,3,3,5,3,1,3,4,...] | 0.64624543989481330426647339684579279 | ||||
1.11072 07345 39591 56175 [Mw 74] | The ratio of a square and circle circumscribed [90] | sum[n=1 to ∞] {(-1)^(floor( (n-1)/2)) /(2n-1)} |
T | OEIS: A093954 | [1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...] | 1.11072073453959156175397024751517342 | ||||
1.45607 49485 82689 67139 [Mw 75] | Backhouse's constant [91] |
|
1/( FindRoot[0 == 1 Sum[x^n Prime[n], {n, 10000}], {x, {1}}) | OEIS: A072508 | [1;2,5,5,4,1,1,18,1,1,1,1,1,2,13,3,1,2,4,16,...] | 1995 | 1.45607494858268967139959535111654355 | |||
1.85193 70519 82466 17036 [Mw 76] | Gibbs constant [92] | Sin integral |
|
SinIntegral[Pi] | OEIS: A036792 | [1;1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39,...] | 1.85193705198246617036105337015799136 | |||
0.23571 11317 19232 93137 [Mw 77] | Copeland–Erdős constant [93] | sum[n=1 to ∞] {prime(n) /(n (10^ sum[k=1 to n]{floor (log_10 prime(k))}))} |
A | OEIS: A033308 | [0;4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3,...] | 0.23571113171923293137414347535961677 | ||||
1.52362 70862 02492 10627 [Mw 78] | Fractal dimension of the boundary of the dragon curve [94] | (log((1 (73-6 sqrt(87))^1/3 (73 6 sqrt(87))^1/3) /3))/ log(2))) |
[1;1,1,10,12,2,1,149,1,1,1,3,11,1,3,17,4,1,...] | 1.52362708620249210627768393595421662 | ||||||
1.78221 39781 91369 11177 [Mw 79] | Grothendieck constant [95] | pi/(2 log(1 sqrt(2))) | OEIS: A088367 | [1;1,3,1,1,2,4,2,1,1,17,1,12,4,3,5,10,1,1,3,...] | 1.78221397819136911177441345297254934 | |||||
1.58496 25007 21156 18145 [Mw 80] | Hausdorff dimension, Sierpinski triangle [96] | ( Sum[n=0 to ∞] {1/ (2^(2n 1) (2n 1))})/ (Sum[n=0 to ∞] {1/ (3^(2n 1) (2n 1))}) |
T | OEIS: A020857 | [1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...] | 1.58496250072115618145373894394781651 | ||||
1.30637 78838 63080 69046 [Mw 81] | Mills' constant [97] | Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8) | OEIS: A051021 | [1;3,3,1,3,1,2,1,2,1,4,2,35,21,1,4,4,1,1,3,2,...] | 1947 | 1.30637788386308069046861449260260571 | ||||
2.02988 32128 19307 25004 [Mw 82] | Figure eight knot hyperbolic volume [98] |
|
6 integral[0 to pi/3] {log(1/(2 sin (n)))} |
OEIS: A091518 | [2;33,2,6,2,1,2,2,5,1,1,7,1,1,1,113,1,4,5,1,...] | 2.02988321281930725004240510854904057 | ||||
262 53741 26407 68743 .99999 99999 99250 073 [Mw 83] |
Hermite–Ramanujan constant[99] | e^(π sqrt(163)) | T | OEIS: A060295 | [262537412640768743;1,1333462407511,1,8,1,1,5,...] | 1859 | 262537412640768743.999999999999250073 | |||
1.74540 56624 07346 86349 [Mw 84] | Khinchin harmonic mean [100] |
a1 ... an are elements of a continued fraction [a0; a1, a2, ..., an] |
(log 2)/ (sum[n=1 to ∞] {1/n log(1 1/(n(n 2))} |
OEIS: A087491 | [1;1,2,1,12,1,5,1,5,13,2,13,2,1,9,1,6,1,3,1,...] | 1.74540566240734686349459630968366106 | ||||
1.64872 12707 00128 14684 [Ow 2] | Square root of the number e [101] | Sum[n=0 to ∞] {1/(2^n n!)} |
T | OEIS: A019774 | [1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] = [1;1,1,1,4p 1], p∈ℕ |
1.64872127070012814684865078781416357 | ||||
1.01734 30619 84449 13971 [Mw 85] | Zeta(6) [102] | Prod[n=1 to ∞] {1/(1-ithprime (n)^-6)} |
T | OEIS: A013664 | [1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...] | 1.01734306198444913971451792979092052 | ||||
0.10841 01512 23111 36151 [Mw 86] | Trott constant [103] |
|
Trott Constant | OEIS: A039662 | [0;9,4,2,5,1,2,2,3,1,1,1,3,6,1,5,1,1,2,...] | 0.10841015122311136151129081140641509 | ||||
0.00787 49969 97812 3844 [Mw 87] | Chaitin constant [104] | See also: Halting problem |
T | OEIS: A100264 | [0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1] | 1975 | 0.0078749969978123844 | |||
0.83462 68416 74073 18628 [Mw 88] | Gauss constant [105] | (4 sqrt(2)((1/4)!)^2) /pi^(3/2) |
T | OEIS: A014549 | [0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...] | 0.83462684167407318628142973279904680 | ||||
1.45136 92348 83381 05028 [Mw 89] | Ramanujan–Soldner constant[106][107] | li = Logarithmic integral Ei = Exponential integral |
FindRoot[li(x) = 0] | I | OEIS: A070769 | [1;2,4,1,1,1,3,1,1,1,2,47,2,4,1,12,1,1,2,2,1,...] | 1792 to 1809 |
1.45136923488338105028396848589202744 | ||
0.64341 05462 88338 02618 [Mw 90] | Cahen's constant [108] |
Where sk is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ...
|
T | OEIS: A080130 | [0; 1, 1, 1, 4, 9, 196, 16641, 639988804, ...] | 1891 | 0.64341054628833802618225430775756476 | |||
1.41421 35623 73095 04880 [Mw 91] | Square root of 2, Pythagoras constant.[109] | prod[n=1 to ∞] {1 (-1)^(n 1) /(2n-1)} |
A | OEIS: A002193 | [1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...] = [1;2...] |
1.41421356237309504880168872420969808 | ||||
1.77245 38509 05516 02729 [Mw 92] | Carlson–Levin constant [110] | sqrt (pi) | T | OEIS: A002161 | [1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...] | 1.77245385090551602729816748334114518 | ||||
1.08636 30943 59295 26456 [Ow 3] | Musical interval between each half tone [111][112] |
|
2^(1/12) | A | OEIS: A010774 | [1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...] | 1.08636309435929526456182529494634170 | |||
1.01494 16064 09653 62502 [Mw 93] | Gieseking constant [113] | . |
sqrt(3)*3/4 *(1 -Sum[n=0 to ∞] {1/((3n 2)^2)} Sum[n=1 to ∞] {1/((3n 1)^2)}) |
OEIS: A143298 | [1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...] | 1912 | 1.01494160640965362502120255427452028 | |||
2.62205 75542 92119 81046 [Mw 94] | Lemniscate constant [114] | 4 sqrt(2/pi) ((1/4)!)^2 |
T | OEIS: A062539 | [2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...] | 1798 | 2.62205755429211981046483958989111941 | |||
1.28242 71291 00622 63687 [Mw 95] | Glaisher–Kinkelin constant [115] | e^(1/12-zeta´{-1}) | T ? | OEIS: A074962 | [1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...] | 1.28242712910062263687534256886979172 | ||||
-4.22745 35333 76265 408 [Mw 96] | Digamma (1/4) [116] | -EulerGamma -\pi/2 -3 log 2 |
OEIS: A020777 | -[4;4,2,1,1,10,1,5,9,11,1,22,1,1,14,1,2,1,4,...] | -4.2274535333762654080895301460966835 | |||||
0.28674 74284 34478 73410 [Mw 97] | Strongly Carefree constant [117] | N[ prod[k=1 to ∞] {1-(3*prime(k)-2) /(prime(k)^3)}] |
OEIS: A065473 | [0;3,2,19,3,12,1,5,1,5,1,5,2,1,1,1,1,1,3,7,...] | 0.28674742843447873410789271278983845 | |||||
1.78107 24179 90197 98523 [Mw 98] | Exp.gamma, Barnes G-function [118] |
|
Prod[n=1 to ∞] {e^(1/n)} /{1 1/n} |
OEIS: A073004 | [1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...] | 1.78107241799019798523650410310717954 | ||||
3.62560 99082 21908 31193 [Mw 99] | Gamma(1/4)[119] | 4(1/4)! | T | OEIS: A068466 | [3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...] | 1729 | 3.62560990822190831193068515586767200 | |||
1.66168 79496 33863 12129 [Mw 100] | Somos' quadratic recurrence constant [120] | prod[n=1 to ∞] {n ^(1/2)^n} |
T ? | OEIS: A065481 | [1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...] | 1.66168794963386312129581892274995074 | ||||
0.95531 66181 245092 78163 | Magic angle [121] | arctan(sqrt(2)) | I | OEIS: A195696 | [0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3,...] | 0.95531661812450927816385710251575775 | ||||
0.74759 79202 53411 43517 [Mw 101] | Rényi's Parking Constant [122] | [e^(-2*Gamma)] * Int{n,0,∞}[ e^(- 2 *Gamma(0,n)) /n^2] |
OEIS: A050996 | [0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...] | 0.74759792025341143517873094383017817 | |||||
1.44466 78610 09766 13365 [Mw 102] | Steiner number, Iterated exponential Constant [123] | = Upper Limit of Tetration | e^(1/e) | T | OEIS: A073229 | [1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...] | 1.44466786100976613365833910859643022 | |||
0.69220 06275 55346 35386 [Mw 103] | Minimum value of función ƒ(x) = xx [124] |
= Inverse Steiner Number | e^(-1/e) | OEIS: A072364 | [0;1,2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...] | 0.69220062755534635386542199718278976 | ||||
0.34053 73295 50999 14282 [Mw 104] | Pólya Random walk constant [125] |
|
1-16*Sqrt[2/3]*Pi^3 /(Gamma[1/24] *Gamma[5/24] *Gamma[7/24] *Gamma[11/24]) |
OEIS: A086230 | [0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...] | 0.34053732955099914282627318443290289 | ||||
0.54325 89653 42976 70695 [Mw 105] | Bloch–Landau constant [126] | gamma(1/3) *gamma(5/6) /gamma(1/6) |
OEIS: A081760 | [0;1,1,5,3,1,1,2,1,1,6,3,1,8,11,2,1,1,27,4,...] | 1929 | 0.54325896534297670695272829530061323 | ||||
0.18785 96424 62067 12024 [Mw 106] [Ow 4] | MRB Constant, Marvin Ray Burns [127][128][129] | Sum[n=1 to ∞] {(-1)^n (n^(1/n)-1)} |
OEIS: A037077 | [0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...] | 1999 | 0.18785964246206712024851793405427323 | ||||
1.27323 95447 35162 68615 | Ramanujan–Forsyth series[130] | Sum[n=0 to ∞] {[(2n-3)!! /(2n)!!]^2} |
I | OEIS: A088538 | [1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...] | 1.27323954473516268615107010698011489 | ||||
1.46707 80794 33975 47289 [Mw 107] | Porter Constant[131] |
|
6*ln2/pi^2(3*ln2 4 EulerGamma- WeierstrassZeta'(2) *24/pi^2-2)-1/2 | OEIS: A086237 | [1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...] | 1974 | 1.46707807943397547289779848470722995 | |||
4.66920 16091 02990 67185 [Mw 108] | Feigenbaum constant δ [132] |
|
T | OEIS: A006890 | [4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...] | 1975 | 4.66920160910299067185320382046620161 | |||
2.50290 78750 95892 82228 [Mw 109] | Feigenbaum constant α[133] | T ? | OEIS: A006891 | [2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...] | 1979 | 2.50290787509589282228390287321821578 | ||||
0.62432 99885 43550 87099 [Mw 110] | Golomb–Dickman constant [134] | N[Int{n,0,1}[e^Li(n)],34] | OEIS: A084945 | [0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...] | 1930 & 1964 |
0.62432998854355087099293638310083724 | ||||
23.14069 26327 79269 0057 [Mw 111] | Gelfond constant [135] | Sum[n=0 to ∞] {(pi^n)/n!} |
T | OEIS: A039661 | [23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...] | 23.1406926327792690057290863679485474 | ||||
7.38905 60989 30650 22723 | Conic constant, Schwarzschild constant [136] | Sum[n=0 to ∞] {2^n/n!} |
OEIS: A072334 | [7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...] = [7,2,1,1,n,4*n 6,n 2], n = 3, 6, 9, etc. |
7.38905609893065022723042746057500781 | |||||
0.35323 63718 54995 98454 [Mw 112] | Hafner–Sarnak–McCurley constant (1) [137] | prod[k=1 to ∞] {1-(1-prod[j=1 to n] {1-ithprime(k)^-j})^2} | OEIS: A085849 | [0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3,...] | 1993 | 0.35323637185499598454351655043268201 | ||||
0.60792 71018 54026 62866 [Mw 113] | Hafner–Sarnak–McCurley constant (2) [138] | Prod{n=1 to ∞} (1-1/ithprime(n)^2) |
T | OEIS: A059956 | [0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...] | 0.60792710185402662866327677925836583 | ||||
0.12345 67891 01112 13141 [Mw 114] | Champernowne constant [139] | T | OEIS: A033307 | [0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...] | 1933 | 0.12345678910111213141516171819202123 | ||||
0.76422 36535 89220 66299 [Mw 115] | Landau-Ramanujan constant [140] | T ? | OEIS: A064533 | [0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...] | 0.76422365358922066299069873125009232 | |||||
1.92878 00... [Mw 116] | Wright constant [141] | OEIS: A086238 | [1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3] | 1.9287800... | ||||||
2.71828 18284 59045 23536 [Mw 117] | Number e, Euler's number [142] | Sum[n=0 to ∞] {1/n!} |
T | OEIS: A001113 | [2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] = [2;1,2p,1], p∈ℕ |
2.71828182845904523536028747135266250 | ||||
0.36787 94411 71442 32159 [Mw 118] | Inverse of Number e [143] | Sum[n=2 to ∞] {(-1)^n/n!} |
T | OEIS: A068985 | [0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,...] = [0;2,1,1,2p,1], p∈ℕ |
1618 | 0.36787944117144232159552377016146086 | |||
0.69034 71261 14964 31946 | Upper iterated exponential [144] | 2^-3^-4^-5^-6^ -7^-8^-9^-10^ -11^-12^-13 … |
OEIS: A242760 | [0;1,2,4,2,1,3,1,2,2,1,4,1,2,4,3,1,1,10,1,3,2,...] | 0.69034712611496431946732843846418942 | |||||
0.65836 55992 ... | Lower límit iterated exponential [145] | 2^-3^-4^-5^-6^ -7^-8^-9^-10^ -11^-12 … |
[0;1,1,1,12,1,2,1,1,4,3,1,1,2,1,2,1,51,2,2,1,...] | 0.6583655992... | ||||||
3.14159 26535 89793 23846 [Mw 119] | π number, Archimedes number [146] | Sum[n=0 to ∞] {(-1)^n 4/(2n 1)} |
T | OEIS: A000796 | [3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...] | 3.14159265358979323846264338327950288 | ||||
0.46364 76090 00806 11621 | Machin–Gregory series[147] | Sum[n=0 to ∞] {(-1)^n (1/2)^(2n 1) /(2n 1)} |
A | OEIS: A073000 | [0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1,...] | 0.46364760950080611621425623146121440 | ||||
1.90216 05831 04 [Mw 120] | Brun 2 constant = Σ inverse of Twin primes [148] | OEIS: A065421 | [1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2] | 1.902160583104 | ||||||
0.87058 83799 75 [Mw 121] | Brun 4 constant = Σ inv.prime quadruplets [149] |
|
OEIS: A213007 | [0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1] | 0.870588379975 | |||||
0.63661 97723 67581 34307 [Mw 122] | Buffon constant[150] | 2/Pi | T | OEIS: A060294 | [0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...] | 1540 to 1603 |
0.63661977236758134307553505349005745 | |||
0.59634 73623 23194 07434 [Mw 123] | Euler–Gompertz constant [151] | integral[0 to ∞] {(e^-n)/(1 n)} |
OEIS: A073003 | [0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...] | 0.59634736232319407434107849936927937 | |||||
Imaginary number [152] | sqrt(-1) | C | 1501 to 1576 |
|||||||
0.69777 46579 64007 98200 [Mw 125] | Continued fraction constant, Bessel function[153] | (Sum [n=0 to ∞] {n/(n!n!)}) / (Sum [n=0 to ∞] {1/(n!n!)}) |
OEIS: A052119 | [0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] = [0;p 1], p∈ℕ |
0.69777465796400798200679059255175260 | |||||
2.74723 82749 32304 33305 | Ramanujan nested radical [154] | (2 sqrt(5) sqrt(15 -6 sqrt(5)))/2 |
A | [2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...] | 2.74723827493230433305746518613420282 | |||||
0.56714 32904 09783 87299 [Mw 126] | Omega constant, Lambert W function [155] | Sum[n=1 to ∞] {(-n)^(n-1)/n!} |
T | OEIS: A030178 | [0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1,...] | 0.56714329040978387299996866221035555 | ||||
0.96894 61462 59369 38048 | Beta(3) [156] | Sum[n=1 to ∞] {(-1)^(n 1) /(-1 2n)^3} |
T | OEIS: A153071 | [0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...] | 0.96894614625936938048363484584691860 | ||||
2.23606 79774 99789 69640 | Square root of 5, Gauss sum [157] | Sum[k=0 to 4] {e^(2k^2 pi i/5)} |
A | OEIS: A002163 | [2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] = [2;4,...] |
2.23606797749978969640917366873127624 | ||||
3.35988 56662 43177 55317 [Mw 127] | Prévost constant Reciprocal Fibonacci constant[158] |
Fn: Fibonacci series |
Sum[n=1 to ∞] {1/Fibonacci[n]} |
I | OEIS: A079586 | [3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...] | ? | 3.35988566624317755317201130291892717 | ||
2.68545 20010 65306 44530 [Mw 128] | Khinchin's constant [159] | Prod[n=1 to ∞] {(1 1/(n(n 2))) ^(ln(n)/ln(2))} |
T | OEIS: A002210 | [2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...] | 1934 | 2.68545200106530644530971483548179569 |
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