This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370742 #8 Jan 05 2025 19:51:42
%S A370742 5,9,6,6,7,3,4,8,7,8,3,3,9,8,2,6,9,7,3,7,7,7,0,6,8,2,4,3,6,8,3,3,0,8,
%T A370742 3,9,2,4,6,8,7,9,6,7,0,4,2,1,8,3,8,8,2,8,2,8,6,6,0,6,1,5,1,7,6,4,1,9,
%U A370742 6,3,6,7,5,0,1,0,6,9,8,1,2,4,3,9,9,1,8,2,3,9,6,8,1,6,1,1,0,9,3,9,6,9,5,3,7
%N A370742 Decimal expansion of Sum_{k>=2} H(k-1) * F(k) / (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.
%H A370742 Kenny B. Davenport, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/ElemProbSolnFeb2018.pdf">Problem B-1222</a>, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 56, No. 1 (2018), p. 81; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Problems/February2019Elem.pdf">The Generating Function for Harmonic Numbers</a>, Solution to Problem B-1222 by Amanda M. Andrews and Samantha L. Zimmerman, ibid., Vol. 57, No. 1 (2019), pp. 83-84.
%F A370742 Equals 4 * log(2) * log(phi) / sqrt(5), where phi is the golden ratio (A001622) (Davenport, 2018).
%e A370742 0.59667348783398269737770682436833083924687967042183...
%t A370742 RealDigits[4 * Log[2] * Log[GoldenRatio] / Sqrt[5], 10, 120][[1]]
%o A370742 (PARI) 4 * log(2) * log(quadgen(5)) / sqrt(5)
%Y A370742 Cf. A000045, A001008, A001622, A002162, A002163, A002390, A002805, A349850, A370743.
%K A370742 nonn,cons,easy
%O A370742 0,1
%A A370742 _Amiram Eldar_, Feb 29 2024