A067616 -id:A067616 - cp's OEIS frontend

A078075 Duplicate of A067616.

1, 7, 3, 1, 1, 4, 57, 2, 3, 1, 5, 1, 3, 1, 2, 3, 9, 1, 2, 9, 3, 1, 18, 7, 1, 2, 6, 2, 1, 35, 2, 1, 5, 84, 3, 2, 7, 1, 1, 1, 28, 2, 1, 2, 1, 2, 3, 1, 2, 19, 1, 17, 1, 1, 8, 4, 3, 1, 81, 7, 1, 154, 24, 1, 65, 7, 3, 5, 94, 7, 1, 1, 8, 32, 3, 1, 1, 1, 3, 8, 2, 2, 2, 1, 5, 1, 2, 1, 1, 1, 7, 1, 5

Offset: 1

Benoit Cloitre, Dec 02 2002

dead

A065443 Decimal expansion of Sum_{k=1..inf} 1/(2^k-1)^2.

Original entry on oeis.org

1, 1, 3, 7, 3, 3, 8, 7, 3, 6, 3, 4, 4, 1, 9, 6, 5, 9, 6, 6, 9, 6, 9, 1, 3, 3, 6, 8, 3, 0, 1, 3, 4, 7, 5, 8, 3, 8, 3, 0, 8, 4, 9, 3, 0, 9, 8, 1, 3, 8, 8, 2, 8, 8, 2, 0, 7, 0, 4, 4, 9, 3, 3, 1, 0, 4, 6, 4, 9, 3, 8, 6, 2, 5, 2, 0, 4, 0, 8, 9, 9, 8, 0, 0, 0, 5, 4, 0, 5, 0, 9, 0, 4, 2, 3, 5, 1, 3, 1, 1, 8, 4, 0, 3, 6

Offset: 1

N. J. A. Sloane, Nov 18 2001

			1.1373387363441965966969133683013475838308493098...

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

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]
Eric Weisstein's World of Mathematics, Tree Searching.

Cf. A060867, A065442, A065608, A066766, A067616.

RealDigits[NSum[1/(2^k - 1)^2, {k, 1, Infinity}, PrecisionGoal -> 40, AccuracyGoal -> 40, WorkingPrecision -> 500, NSumTerms -> 50, NSumExtraTerms -> 50]][[1]] (* Peter Bertok (peter(AT)bertok.com), Dec 04 2001 *)
RealDigits[(Log[2] QPolyGamma[0, 1, 1/2] + QPolyGamma[1, 1, 1/2])/Log[2]^2 - 1, 10, 20][[1]] (* Eric W. Weisstein, Jun 02 2025 *)

{ default(realprecision, 2080); x=suminf(k=1, 1/(2^k - 1)^2); for (n=1, 2000, d=floor(x); x=(x-d)*10; write("b065443.txt", n, " ", d)) } \\ Harry J. Smith, Oct 19 2009

Equals Sum_{n>=1} 1/A060867(n).
From Amiram Eldar, Oct 16 2022: (Start)
Equals Sum_{k>=1} k/(2^(k+1)-1).
Equals A066766 - A065442. (End)
Equals Sum_{n >= 1} q^(n^2)*( (n - 1) + q^n - (n - 1)*q^(2*n) )/(1 - q^n)^2 evaluated at q = 1/2 (see A065608). - Peter Bala, Oct 16 2022

More terms from Peter Bertok (peter(AT)bertok.com), Dec 04 2001

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A078075 Duplicate of A067616.

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A065443 Decimal expansion of Sum_{k=1..inf} 1/(2^k-1)^2.

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