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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
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
OFFSET
1,2
LINKS
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]]
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Feb 19 2022
STATUS
approved