A351789 - OEIS

A351789

Decimal expansion of Sum_{k>=1} AH(k)*F(k)/2^k, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic number and F(k) = A000045(k) is the k-th Fibonacci number.

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

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OFFSET

1,2

LINKS

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

Seán M. Stewart, Problem H-893, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 60, No. 1 (2022), p. 91.

FORMULA

Equals log(5/4) + 6*log(phi)/sqrt(5), where phi is the golden ratio (A001622) (Stewart, 2022).

EXAMPLE

1.51437037420622187243459478916165077964831313316887...

MATHEMATICA

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