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A100220 Decimal expansion of Product_{k>=1} (1-1/3^k). 26
5, 6, 0, 1, 2, 6, 0, 7, 7, 9, 2, 7, 9, 4, 8, 9, 4, 4, 9, 6, 9, 7, 9, 2, 2, 4, 3, 3, 1, 4, 1, 4, 0, 0, 1, 4, 3, 7, 9, 7, 3, 6, 3, 3, 3, 7, 9, 8, 3, 6, 2, 4, 6, 4, 4, 6, 2, 9, 5, 6, 2, 9, 7, 3, 1, 7, 5, 3, 3, 9, 6, 3, 0, 8, 9, 0, 3, 3, 7, 9, 4, 7, 0, 7, 7, 1, 6, 9, 1, 8, 7, 7, 0, 5, 3, 6, 7, 4, 3, 3, 4, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

0.560126077... = limit of the probability that a random N X N matrix, with entries chosen independently and uniformly from the field F_3, is nonsingular [Morrison (2006)]. - L. Edson Jeffery, Jan 22 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1200

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Eric Weisstein's World of Mathematics, Infinite Product

FORMULA

exp(-sum{k>0, sigma_1(k)/k/3^k})=exp(-sum{k>0, A000203(k)/k/3^k}). - Hieronymus Fischer, Aug 07 2007

Product_{k >=1} (1-1/3^k) = (1/3; 1/3)_{infinity}, where (a;q)_{infinity} is the q-Pochhammer symbol. - G. C. Greubel, Nov 27 2015

EXAMPLE

0.560126077...

MATHEMATICA

(3^(1/24)*EllipticThetaPrime[1, 0, 1/Sqrt[3]]^(1/3))/2^(1/3).

N[QPochhammer[1/3, 1/3]] (* G. C. Greubel, Nov 27 2015 *)

CROSSREFS

Cf. A048651, A027871.

Cf. A000203, A100221, A100222, A132019, A132034, A132035, A132036, A132037, A132038, A258458.

Sequence in context: A021645 A031364 A201591 * A011440 A242055 A178591

Adjacent sequences:  A100217 A100218 A100219 * A100221 A100222 A100223

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Nov 09 2004

STATUS

approved

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Last modified June 22 23:15 EDT 2017. Contains 288633 sequences.