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

1,2

Links

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

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 log(2)^2 + 4*log(phi)^2, where phi is the golden ratio (A001622) (Davenport, 2018).

Example

1.40671229622697899465481881125279601179617835179174...

Mathematica

RealDigits[Log[2]^2 + 4*Log[GoldenRatio]^2, 10, 120][[1]]

Prog

(PARI) log(2)^2 + 4*log(quadgen(5))^2

Crossrefs

Cf. A000032, A001008, A001622, A002162, A002390, A002805, A349851, A370742.

Sequence in context: A066760 A102393 A228131 * A019833 A362219 A333479

Adjacent sequences: A370740 A370741 A370742 * A370744 A370745 A370746

Keyword

nonn,cons,easy

Author

Amiram Eldar, Feb 29 2024

Status

approved