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 A367309 #12 Nov 26 2023 09:18:39
%S A367309 6,0,2,1,1,2,3,4,9,3,1,0,3,7,1,5,5,4,9,7,1,1,2,6,3,2,0,0,5,1,5,4,1,3,
%T A367309 5,9,9,4,8,4,7,1,2,0,0,0,0,0,6,3,9,4,6,5,9,6,7,3,6,5,2,6,3,5,8,3,0,8,
%U A367309 2,6,8,1,4,1,8,7,7,3,7,5,7,1,8,5,6,4
%N A367309 Decimal expansion of area under the curve (1-2^(1-x))*zeta(x) from 0 to 1.
%C A367309 The series Sum_{n >= 1} (-1)^(n+1)/n^x converges nonuniformly to g(x) = (1 - 2^(1-x))*zeta(x) on the open interval (0, 1). This series can be described as an alternating version of the 'p-series' when 0 < p < 1. Let f(x) = Sum_{n >= 1} (-1)^(n+1)/n^x. Then f(0+) = g(0) = 1/2 and f(1) = log(2), whereas g(1) is undefined, but has the limit value log(2). Also, f(1/2) = g(1/2) = A113024 = 0.604898643421... .
%e A367309 0.60211234931037155497112632...
%t A367309 y = NIntegrate[(1 - 2^(1-x)) Zeta[x], {x, 0, 1}, WorkingPrecision -> 200]
%t A367309 RealDigits[y][[1]]
%o A367309 (PARI) intnum(x=0, 1, (1-2^(1-x))*zeta(x)) \\ _Michel Marcus_, Nov 14 2023
%Y A367309 Cf. A113024, A367310, A367311.
%K A367309 nonn,cons
%O A367309 0,1
%A A367309 _Alejandro Malla_, Nov 13 2023