A065446 Decimal expansion of Product_{k>=1} (1-1/2^k)^(-1).

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, 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, 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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.

Links

Harry J. Smith, Table of n, a(n) for n=1..2000

Steven R. Finch, Digital Search Tree Constants [Broken link]

Steven R. Finch, Digital Search Tree Constants [From the Wayback machine]

Igor Pak, Greta Panova, and Damir Yeliussizov, On the largest Kronecker and Littlewood-Richardson coefficients, arXiv:1804.04693 [math.CO], 2018. [p. 13]

Jonathan Sondow and Eric W. Weisstein, MathWorld: Wallis Formula.

Formula

Equals Sum_{n>=0} 1/A002884(n)*Product_{j=1..n} 2^n/(2^n-1). - Geoffrey Critzer, Jun 30 2017

Equals 1/QPochhammer(1/2, 1/2)_{infinity}. - G. C. Greubel, Jan 18 2018

Equals 1 + Sum_{n>=1} 2^(n*(n-1)/2)/((2-1)*(2^2-1)*...*(2^n-1)). - Robert FERREOL, Feb 22 2020

Equals 1 / A048651 (constant). - Hugo Pfoertner, Nov 28 2020

Equals Sum_{n>=0} A000041(n)/2^n. - Amiram Eldar, Jan 19 2021

Example

3.46274661945506361153795734292443116454075790290...

Maple

evalf(1+sum(2^(n*(n-1)/2)/product(2^k-1, k=1..n), n=1..infinity), 120); # Robert FERREOL, Feb 22 2020

Mathematica

N[ Product[ 1/(1 - 1/2^k), {k, 1, Infinity} ], 500 ]
RealDigits[1/QPochhammer[1/2, 1/2], 10, 100][[1]] (* Vaclav Kotesovec, Jun 22 2014 *)

Prog

(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
(PARI) prodinf(k=1, 1/(1-1/2^k)) \\ Michel Marcus, Feb 22 2020

Crossrefs

Cf. A000041, A002884, A048651, A048652, A006099.

Sequence in context: A066977 A007551 A161012 * A159962 A214871 A055173

Adjacent sequences: A065443 A065444 A065445 * A065447 A065448 A065449

Keyword

nonn,cons

Author

N. J. A. Sloane, Nov 18 2001

Extensions

More terms from Robert G. Wilson v, Nov 19 2001

Further terms from Vladeta Jovovic, Dec 01 2001

Status

approved