A370743 Decimal expansion of Sum_{k>=2} H(k-1) * L(k) / (k*2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and L(k) = A000032(k) is the k-th Lucas number.
1, 4, 0, 6, 7, 1, 2, 2, 9, 6, 2, 2, 6, 9, 7, 8, 9, 9, 4, 6, 5, 4, 8, 1, 8, 8, 1, 1, 2, 5, 2, 7, 9, 6, 0, 1, 1, 7, 9, 6, 1, 7, 8, 3, 5, 1, 7, 9, 1, 7, 4, 1, 0, 7, 0, 1, 2, 8, 0, 6, 9, 0, 4, 8, 3, 8, 2, 8, 4, 6, 7, 6, 4, 5, 2, 7, 6, 8, 1, 7, 2, 4, 1, 4, 0, 1, 6, 6, 4, 5, 1, 7, 8, 9, 4, 8, 0, 5, 7, 1, 1, 5, 5, 6, 8
Offset: 1
Examples
1.40671229622697899465481881125279601179617835179174...
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[Log[2]^2 + 4*Log[GoldenRatio]^2, 10, 120][[1]]
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PARI
log(2)^2 + 4*log(quadgen(5))^2
Formula
Equals log(2)^2 + 4*log(phi)^2, where phi is the golden ratio (A001622) (Davenport, 2018).