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A349850
Decimal expansion of Sum_{k>=1} H(k)*F(k)/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and F(k) = A000045(k) is the k-th Fibonacci number.
4
3, 9, 6, 8, 7, 4, 8, 0, 0, 6, 9, 0, 3, 9, 1, 4, 8, 5, 2, 1, 7, 1, 0, 6, 3, 6, 4, 0, 6, 1, 9, 9, 8, 5, 6, 8, 8, 6, 9, 8, 4, 2, 4, 3, 6, 3, 9, 6, 2, 2, 4, 8, 4, 3, 6, 7, 8, 3, 3, 9, 6, 6, 4, 2, 9, 4, 2, 1, 5, 4, 5, 3, 6, 7, 0, 6, 1, 8, 1, 1, 9, 9, 3, 8, 0, 6, 6, 8, 2, 4, 2, 1, 7, 6, 1, 5, 7, 1, 0, 7, 5, 2, 1, 9, 8
OFFSET
1,1
LINKS
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(4*phi^(12/sqrt(5))) = 2*log(2) + 12*log(phi)/sqrt(5), where phi is the golden ratio (A001622).
EXAMPLE
3.96874800690391485217106364061998568869842436396224...
MATHEMATICA
RealDigits[2*Log[2] + 12*Log[GoldenRatio]/Sqrt[5], 10, 100][[1]]
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Dec 02 2021
STATUS
approved