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.

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, 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, 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

Offset

1,1

References

K. Ramachandra and R. Sitaramachandrarao, On series, integrals and continued fractions - II, Madras Univ. J., Sect. B, 51 (1988), pp. 181-198.

Links

Table of n, a(n) for n=1..105.

K. Ramachandra, On series integrals and continued fractions I, Hardy-Ramanujan Journal, Vol. 4 (1981), pp. 1-11.

K. Ramachandra, On series, integrals and continued fractions, III, Acta Arithmetica, Vol. 99, No. 3 (2001), pp. 257-266.

Formula

Equals zeta(3) + (Pi^2*log(2) + log(2)^3)/3.

Example

3.59342794177494296025518240703339219591695480351933...

Mathematica

RealDigits[Zeta[3] + (Pi^2*Log[2] + Log[2]^3)/3, 10, 120][[1]]

Prog

(PARI) zeta(3) + (Pi^2*log(2) + log(2)^3)/3

Crossrefs

Cf. A001008, A002805.

Cf. A000796, A002117, A002162, A352769.

Related constants: A152648, A152649, A152651, A218505, A233090, A238168, A238181, A238182, A241753, A244667, A253191, A256988, A345203.

Sequence in context: A200510 A388782 A138055 * A236556 A189044 A299793

Adjacent sequences: A384454 A384455 A384456 * A384458 A384459 A384460

Keyword

nonn,cons,easy

Author

Amiram Eldar, May 30 2025

Status

approved