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Decimal expansion of Sum_{k=1..inf} 1/(2^k-1)^2.
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%I #30 Oct 23 2022 23:33:26

%S 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,

%T 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,

%U 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

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

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

%H Harry J. Smith, <a href="/A065443/b065443.txt">Table of n, a(n) for n=1..2000</a>

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/dig/dig.html">Digital Search Tree Constants</a>. [Broken link]

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TreeSearching.html">Tree Searching</a>.

%F Equals Sum_{n>=1} 1/A060867(n).

%F From _Amiram Eldar_, Oct 16 2022: (Start)

%F Equals Sum_{k>=1} k/(2^(k+1)-1).

%F Equals A066766 - A065442. (End)

%F 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

%e 1.1373387363441965966969133683013475838308493098...

%t 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 *)

%o (PARI) { 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

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

%K nonn,cons

%O 1,3

%A _N. J. A. Sloane_, Nov 18 2001

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