A349851 Decimal expansion of Sum_{k>=1} H(k)*L(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.

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

Offset

1,1

Links

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

Hideyuki Ohtsuka, Problem B-1200, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 54, No. 4 (2016), p. 367; Harmonic and Fiboancci [sic]/Lucas Numbers, Solution to Problem B-1200 by Kenny B. Davenport, ibid., Vol. 55, No. 4 (2017), pp. 372-373.

Formula

Equals log(64*phi^(4*sqrt(5))) = 6*log(2) + 4*sqrt(5)*log(phi), where phi is the golden ratio (A001622).

Example

8.46297249299971224539772505825511366269870763156442...

Mathematica

RealDigits[6*Log[2] + 4*Sqrt[5]*Log[GoldenRatio], 10, 100][[1]]

Crossrefs

Cf. A000032, A001008, A001622, A002162, A002390, A002805, A349850.

Sequence in context: A178727 A354917 A243446 * A347328 A154188 A198500

Adjacent sequences: A349848 A349849 A349850 * A349852 A349853 A349854

Keyword

nonn,cons,changed

Author

Amiram Eldar, Dec 02 2021

Status

approved