A370742 Decimal expansion of Sum_{k>=2} H(k-1) * F(k) / (k*2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and F(k) = A000045(k) is the k-th Fibonacci number.

5, 9, 6, 6, 7, 3, 4, 8, 7, 8, 3, 3, 9, 8, 2, 6, 9, 7, 3, 7, 7, 7, 0, 6, 8, 2, 4, 3, 6, 8, 3, 3, 0, 8, 3, 9, 2, 4, 6, 8, 7, 9, 6, 7, 0, 4, 2, 1, 8, 3, 8, 8, 2, 8, 2, 8, 6, 6, 0, 6, 1, 5, 1, 7, 6, 4, 1, 9, 6, 3, 6, 7, 5, 0, 1, 0, 6, 9, 8, 1, 2, 4, 3, 9, 9, 1, 8, 2, 3, 9, 6, 8, 1, 6, 1, 1, 0, 9, 3, 9, 6, 9, 5, 3, 7

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Kenny B. Davenport, Problem B-1222, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 56, No. 1 (2018), p. 81; The Generating Function for Harmonic Numbers, Solution to Problem B-1222 by Amanda M. Andrews and Samantha L. Zimmerman, ibid., Vol. 57, No. 1 (2019), pp. 83-84.

Formula

Equals 4 * log(2) * log(phi) / sqrt(5), where phi is the golden ratio (A001622) (Davenport, 2018).

Example

0.59667348783398269737770682436833083924687967042183...

Mathematica

RealDigits[4 * Log[2] * Log[GoldenRatio] / Sqrt[5], 10, 120][[1]]

Prog

(PARI) 4 * log(2) * log(quadgen(5)) / sqrt(5)

Crossrefs

Cf. A000045, A001008, A001622, A002162, A002163, A002390, A002805, A349850, A370743.

Sequence in context: A266564 A201589 A198349 * A176110 A262974 A319757

Adjacent sequences: A370739 A370740 A370741 * A370743 A370744 A370745

Keyword

nonn,cons,easy

Author

Amiram Eldar, Feb 29 2024

Status

approved