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
Examples
0.59667348783398269737770682436833083924687967042183...
Links
- 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.
Programs
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Mathematica
RealDigits[4 * Log[2] * Log[GoldenRatio] / Sqrt[5], 10, 120][[1]]
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PARI
4 * log(2) * log(quadgen(5)) / sqrt(5)
Formula
Equals 4 * log(2) * log(phi) / sqrt(5), where phi is the golden ratio (A001622) (Davenport, 2018).