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A065446 Decimal expansion of Product_{k>=1} (1-1/2^k)^(-1). 14
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 (list; constant; graph; refs; listen; history; text; internal format)
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, Damir Yeliussizov, On the largest Kronecker and Littlewood-Richardson coefficients, arXiv:1804.04693 [math.CO], 2018. [p. 13]

J. Sondow and E. 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

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. 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

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Last modified July 12 23:28 EDT 2020. Contains 335669 sequences. (Running on oeis4.)