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 A357053 #12 Feb 16 2025 08:34:04
%S A357053 2,3,9,7,4,1,4,1,8,7,9,1,6,5,2,1,2,0,0,4,0,9,2,2,4,4,9,5,6,8,1,7,7,8,
%T A357053 7,0,8,5,2,0,7,2,2,2,9,6,3,7,5,5,4,4,4,8,5,8,3,1,9,7,3,7,0,8,7,2,8,2,
%U A357053 3,7,7,7,8,9,3,2,2,1,5,9,9,2,3,2,8,7,6,1,8,6,8,5,6,7,0,3,3,6,6,5,1,0,8,4,9
%N A357053 Decimal expansion of Sum_{k>=1} k/Fibonacci(2*k).
%C A357053 This constant is transcendental (Duverney et al., 1998).
%D A357053 Daniel Duverney, Keiji Nishioka, Kumiko Nishioka, and Iekata Shiokawa, Transcendence of Jacobi's theta series and related results, in: K. Györy, et al. (eds.), Number Theory, Diophantine, Computational and Algebraic Aspects, Proceedings of the International Conference held in Eger, Hungary, July 29-August 2, 1996, de Gruyter, 1998, pp. 157-168.
%H A357053 Daniel Duverney and Iekata Shiokawa, <a href="https://doi.org/10.1063/1.2841912">On series involving Fibonacci and Lucas numbers I</a>, AIP Conference Proceedings, Vol. 976, No. 1. American Institute of Physics, 2008, pp. 62-76.
%H A357053 Derek Jennings, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/32-1/jennings.pdf">On reciprocals of Fibonacci and Lucas numbers</a>, Fibonacci Quarterly, Vol. 32, No. 1 (1994), pp. 18-21.
%H A357053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JacobiThetaFunctions.html">Jacobi Theta Functions</a>.
%H A357053 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A357053 Equals Sum_{k>=1} k/A001906(k).
%F A357053 Equals sqrt(5) * Sum_{k>=1} 1/Lucas(2*k-1)^2 (Jennings, 1994).
%F A357053 Equals (1/2)*(1/phi^4 - 1)*theta_4'(1/phi^2)/theta_4(1/phi^2), where phi is the golden ratio (A001622) and theta_4 is a Jacobi theta function.
%e A357053 2.39741418791652120040922449568177870852072229637554...
%t A357053 RealDigits[Sum[k/Fibonacci[2*k], {k, 1, 300}], 10, 100][[1]]
%o A357053 (PARI) sumpos(k=1, k/fibonacci(2*k)) \\ _Michel Marcus_, Sep 10 2022
%Y A357053 Cf. A000045, A001622, A001906, A002448, A002878, A081071, A357054.
%Y A357053 Cf. A079586, A153386, A153387.
%K A357053 nonn,cons
%O A357053 1,1
%A A357053 _Amiram Eldar_, Sep 10 2022