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User:RazrRekr201/Table of constants

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Table of constants and other irrational or transcendental numbers

[edit]
Value Name Graphics Symbol LaTeX Formula 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))}]
OEISA065463 [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 OEISA179260 [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 .

OEISA038517 [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 OEISA069196 [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 OEISA065442 [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 OEISA001622 [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 OEISA013661 [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 OEISA002194 [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]]]
OEISA072449 [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 OEISA103710 [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]




ø() = Euler's totient function, σ1() = Divisor function.
Sum[n=1 to ∞]
{1/[EulerPhi(n)
DivisorSigma(1,n)]}
OEISA093827 [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 OEISA104956 [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 ? OEISA065493 [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
Γ() = Gamma function
3×Gamma(1/3)
^3/(4 pi^2)
OEISA224273 [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] OEISA086088 [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 OEISA243309 [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))}
OEISA033150 [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.
Dirichlet series
Sum[1/(n
Binomial[2 n, n])
, {n, 1, ∞}]
T OEISA073010 [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
OEISA246724
[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 OEISA014571 [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 ? OEISA141848 [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
OEISA033259 [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]] OEISA143301 [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 OEISA046095 [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)! OEISA068465 [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 OEISA010774 [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 OEISA006752 [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 OEISA003881 [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 ? OEISA118228 [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^...) OEISA212479 [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}
OEISA083648 [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)}
OEISA073009 [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)})
OEISA064648 [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 OEISA086203 [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 OEISA086201 [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}]
OEISA143233 [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 OEISA212877
OEISA212878
[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 OEISA007493 [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 ? OEISA065476 [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 OEISA068996 [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))]
OEISA213080 [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 ]
OEISA064853 [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
OEISA073012 [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 OEISA014715 [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) OEISA100199 [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)}
OEISA113476 [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 ...
OEISA082839 [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)]
OEISA243277 [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 OEISA062546 [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
OEISA085361 [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,

OEISA085848 [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
OEISA085846 [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 OEISA072691 [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 OEISA002162 [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)
OEISA094692 [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)}
OEISA001620 [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))
OEISA242710 [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) OEISA212224 [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 ? OEISA065478 [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 OEISA003957 [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 ? OEISA175639 [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) OEISA093341 [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)} OEISA242623 [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))}
OEISA226317 [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 OEISA010503 [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}
OEISA085291 [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]]
OEISA062089 [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))
OEISA098907 [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 OEISA226654 [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 OEISA116425 [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)
OEISA082695 [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 OEISA011003 [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 OEISA013662 [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 OEISA222133 [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 OEISA060006 [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 OEISA174606 [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]
OEISA143347 [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}
OEISA123852 [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 ? OEISA077761 [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 OEISA042972 [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 OEISA010527 - [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 OEISA012245 [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) OEISA073230 [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 OEISA058265 [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 OEISA073233 [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-
OEISA059750
[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!}
OEISA073226 [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]])
OEISA086057 [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 OEISA093954 [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}}) OEISA072508 [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] OEISA036792 [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 OEISA033308 [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))) OEISA088367 [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 OEISA020857 [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) OEISA051021 [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)))}
OEISA091518 [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 OEISA060295 [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))}
OEISA087491 [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 OEISA019774 [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 OEISA013664 [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 OEISA039662 [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 OEISA100264 [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]

AGM = Arithmetic–geometric mean

(4 sqrt(2)((1/4)!)^2)
/pi^(3/2)
T OEISA014549 [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 OEISA070769 [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, ...
Defined as:

T OEISA080130 [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 OEISA002193 [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 OEISA002161 [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 OEISA010774 [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)})
OEISA143298 [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 OEISA062539 [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 ? OEISA074962 [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
OEISA020777 -[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)}]
OEISA065473 [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}
OEISA073004 [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 OEISA068466 [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 ? OEISA065481 [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 OEISA195696 [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]
OEISA050996 [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 OEISA073229 [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) OEISA072364 [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])
OEISA086230 [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)
OEISA081760 [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)}
OEISA037077 [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 OEISA088538 [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 OEISA086237 [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 OEISA006890 [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 ? OEISA006891 [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] OEISA084945 [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 OEISA039661 [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!}
OEISA072334 [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} OEISA085849 [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 OEISA059956 [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 OEISA033307 [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 ? OEISA064533 [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]


OEISA086238 [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 OEISA001113 [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 OEISA068985 [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 …
OEISA242760 [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 OEISA000796 [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 OEISA073000 [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] OEISA065421 [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]



OEISA213007 [0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1] 0.870588379975
0.63661 97723 67581 34307 [Mw 122]

[Ow 5]

Buffon constant[150]

Viète product

2/Pi T OEISA060294 [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)}
OEISA073003 [0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...] 0.59634736232319407434107849936927937
i ··· [Mw 124]
Imaginary number [152] sqrt(-1) C 1501
to
1576
i
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!)})
OEISA052119 [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 OEISA030178 [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 OEISA153071 [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 OEISA002163 [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 OEISA079586 [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 OEISA002210 [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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