This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065443 #35 Jun 02 2025 08:20:17
%S A065443 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 A065443 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 A065443 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 A065443 Decimal expansion of Sum_{k=1..inf} 1/(2^k-1)^2.
%D A065443 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 354-361.
%H A065443 Harry J. Smith, <a href="/A065443/b065443.txt">Table of n, a(n) for n=1..2000</a>
%H A065443 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/dig/dig.html">Digital Search Tree Constants</a>. [Broken link]
%H A065443 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 A065443 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TreeSearching.html">Tree Searching</a>.
%F A065443 Equals Sum_{n>=1} 1/A060867(n).
%F A065443 From _Amiram Eldar_, Oct 16 2022: (Start)
%F A065443 Equals Sum_{k>=1} k/(2^(k+1)-1).
%F A065443 Equals A066766 - A065442. (End)
%F A065443 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 A065443 1.1373387363441965966969133683013475838308493098...
%t A065443 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 *)
%t A065443 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 *)
%o A065443 (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 A065443 Cf. A060867, A065442, A065608, A066766, A067616.
%K A065443 nonn,cons
%O A065443 1,3
%A A065443 _N. J. A. Sloane_, Nov 18 2001
%E A065443 More terms from Peter Bertok (peter(AT)bertok.com), Dec 04 2001