A351794 Decimal expansion of Sum_{k>=1} AH(k)*L(k)/2^k, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic number and L(k) = A000032(k) is the k-th Lucas number.

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

Offset: 1

Author

Amiram Eldar, Feb 19 2022

Keywords

• nonn
• cons

Examples

			2.82147535876264946174605143568253063724665666934546...
		

Crossrefs

Cf. A000032, A001622, A002390, A058312, A058313, A349850, A349851, A351789.

Programs

Mathematica

RealDigits[3*Log[5/4] + 10*Log[GoldenRatio]/Sqrt[5], 10, 100][[1]]

Formula

Equals 3*log(5/4) + 10*log(phi)/sqrt(5), where phi is the golden ratio (A001622).

Equals (4/3)*log(5/4) + (5/3)*A351789.