cp's OEIS Frontend

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.

A349641 Decimal expansion of the Sum_{k>=2} 1/(k^3*log(k)).

This page as a plain text file.
%I A349641 #21 Nov 27 2021 12:02:32
%S A349641 2,3,7,9,9,6,1,0,0,1,9,8,6,2,1,3,0,1,9,9,2,8,7,9,0,7,8,3,1,3,3,1,9,0,
%T A349641 6,9,4,9,1,7,3,5,0,7,2,6,1,3,2,4,3,7,9,4,5,5,6,9,7,5,7,7,0,2,7,8,3,0,
%U A349641 0,8,8,8,3,6,3,0,8,0,4,0,0,4,8,6,3,9,0,0,2,8,1,6,2,0,5,4,1,8,5
%N A349641 Decimal expansion of the Sum_{k>=2} 1/(k^3*log(k)).
%F A349641 Equals Integral_{s=3..oo} (zeta(s) - 1) ds.
%e A349641 Sum_{k>=2} 1/(k^3*log(k)) = 0.23799610019862130199...
%t A349641 (* following _Jean-François Alcover_'s Mathematica program for A168218 *) digits = 110; NSum[ 1/(n^3*Log[n]), {n, 2, Infinity}, NSumTerms -> 500000, WorkingPrecision -> digits + 5, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 12}}] // RealDigits[#, 10, digits] & // First
%o A349641 (PARI) intnum(x=3, [oo, log(3)], zeta(x)-1) \\ following _Charles R Greathouse IV_'s program for A168218
%o A349641 (PARI) sumpos(k=2, 1/(k^3*log(k))) \\ _Michel Marcus_, Nov 27 2021
%Y A349641 Similar sequences: A013661, A002117, A073002, A244115, A168218.
%K A349641 nonn,cons
%O A349641 0,1
%A A349641 _Jianing Song_, Nov 24 2021