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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.
3
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
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]]
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Dec 02 2021
STATUS
approved