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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.

%I A351789 #12 Jan 05 2025 19:51:42
%S A351789 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,
%T A351789 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,
%U A351789 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
%N 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.
%H A351789 Seán M. Stewart, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/FebAdvProb2022.pdf">Problem H-893</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 60, No. 1 (2022), p. 91.
%F A351789 Equals log(5/4) + 6*log(phi)/sqrt(5), where phi is the golden ratio (A001622) (Stewart, 2022).
%e A351789 1.51437037420622187243459478916165077964831313316887...
%t A351789 RealDigits[Log[5/4] + 6*Log[GoldenRatio]/Sqrt[5], 10, 100][[1]]
%Y A351789 Cf. A000045, A001622, A002390, A058312, A058313, A349850, A351794.
%K A351789 nonn,cons
%O A351789 1,2
%A A351789 _Amiram Eldar_, Feb 19 2022