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 A384457 #6 May 30 2025 10:35:06
%S A384457 3,5,9,3,4,2,7,9,4,1,7,7,4,9,4,2,9,6,0,2,5,5,1,8,2,4,0,7,0,3,3,3,9,2,
%T A384457 1,9,5,9,1,6,9,5,4,8,0,3,5,1,9,3,3,8,9,3,7,6,9,7,3,8,6,1,1,9,1,8,8,8,
%U A384457 2,8,1,2,6,9,6,1,9,2,6,3,4,0,3,7,3,9,5,7,8,6,7,6,8,6,4,7,4,5,8,7,3,5,5,3,7
%N A384457 Decimal expansion of Sum_{k>=1} H(k)^3/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
%D A384457 K. Ramachandra and R. Sitaramachandrarao, On series, integrals and continued fractions - II, Madras Univ. J., Sect. B, 51 (1988), pp. 181-198.
%H A384457 K. Ramachandra, <a href="https://doi.org/10.46298/hrj.1981.93">On series integrals and continued fractions I</a>, Hardy-Ramanujan Journal, Vol. 4 (1981), pp. 1-11.
%H A384457 K. Ramachandra, <a href="https://doi.org/10.4064/aa99-3-3">On series, integrals and continued fractions, III</a>, Acta Arithmetica, Vol. 99, No. 3 (2001), pp. 257-266.
%F A384457 Equals zeta(3) + (Pi^2*log(2) + log(2)^3)/3.
%e A384457 3.59342794177494296025518240703339219591695480351933...
%t A384457 RealDigits[Zeta[3] + (Pi^2*Log[2] + Log[2]^3)/3, 10, 120][[1]]
%o A384457 (PARI) zeta(3) + (Pi^2*log(2) + log(2)^3)/3
%Y A384457 Cf. A001008, A002805.
%Y A384457 Cf. A000796, A002117, A002162, A352769.
%Y A384457 Related constants: A152648, A152649, A152651, A218505, A233090, A238168, A238181, A238182, A241753, A244667, A253191, A256988, A345203.
%K A384457 nonn,cons,easy
%O A384457 1,1
%A A384457 _Amiram Eldar_, May 30 2025