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%I A065446 #53 Jan 19 2021 05:49:13
%S A065446 3,4,6,2,7,4,6,6,1,9,4,5,5,0,6,3,6,1,1,5,3,7,9,5,7,3,4,2,9,2,4,4,3,1,
%T A065446 1,6,4,5,4,0,7,5,7,9,0,2,9,0,4,4,3,8,3,9,1,3,2,9,3,5,3,0,3,1,7,5,8,9,
%U A065446 1,5,4,3,9,7,4,0,4,2,0,6,4,5,6,8,7,9,2,7,7,4,0,2,9,4,8,4,3,3,5,3,5,0,8,8,0
%N A065446 Decimal expansion of Product_{k>=1} (1-1/2^k)^(-1).
%D A065446 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
%H A065446 Harry J. Smith, <a href="/A065446/b065446.txt">Table of n, a(n) for n=1..2000</a>
%H A065446 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/dig/dig.html">Digital Search Tree Constants</a> [Broken link]
%H A065446 Steven R. Finch, <a href="http://web.archive.org/web/20010413214937/http://www.mathsoft.com:80/asolve/constant/dig/dig.html">Digital Search Tree Constants</a> [From the Wayback machine]
%H A065446 Igor Pak, Greta Panova, and Damir Yeliussizov, <a href="https://arxiv.org/abs/1804.04693">On the largest Kronecker and Littlewood-Richardson coefficients</a>, arXiv:1804.04693 [math.CO], 2018. [p. 13]
%H A065446 Jonathan Sondow and Eric W. Weisstein, <a href="http://mathworld.wolfram.com/WallisFormula.html">MathWorld: Wallis Formula</a>.
%F A065446 Equals Sum_{n>=0} 1/A002884(n)*Product_{j=1..n} 2^n/(2^n-1). - _Geoffrey Critzer_, Jun 30 2017
%F A065446 Equals 1/QPochhammer(1/2, 1/2)_{infinity}. - _G. C. Greubel_, Jan 18 2018
%F A065446 Equals 1 + Sum_{n>=1} 2^(n*(n-1)/2)/((2-1)*(2^2-1)*...*(2^n-1)). - _Robert FERREOL_, Feb 22 2020
%F A065446 Equals 1 / A048651 (constant). - _Hugo Pfoertner_, Nov 28 2020
%F A065446 Equals Sum_{n>=0} A000041(n)/2^n. - _Amiram Eldar_, Jan 19 2021
%e A065446 3.46274661945506361153795734292443116454075790290...
%p A065446 evalf(1+sum(2^(n*(n-1)/2)/product(2^k-1, k=1..n), n=1..infinity), 120); # _Robert FERREOL_, Feb 22 2020
%t A065446 N[ Product[ 1/(1 - 1/2^k), {k, 1, Infinity} ], 500 ]
%t A065446 RealDigits[1/QPochhammer[1/2, 1/2], 10, 100][[1]] (* _Vaclav Kotesovec_, Jun 22 2014 *)
%o A065446 (PARI) { default(realprecision, 2080); x=prodinf(k=1, 1/(1 - 1/2^k)); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065446.txt", n, " ", d)) } \\ _Harry J. Smith_, Oct 19 2009
%o A065446 (PARI) prodinf(k=1, 1/(1-1/2^k)) \\ _Michel Marcus_, Feb 22 2020
%Y A065446 Cf. A000041, A002884, A048651, A048652, A006099.
%K A065446 nonn,cons
%O A065446 1,1
%A A065446 _N. J. A. Sloane_, Nov 18 2001
%E A065446 More terms from _Robert G. Wilson v_, Nov 19 2001
%E A065446 Further terms from _Vladeta Jovovic_, Dec 01 2001

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