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 A365523 #15 Nov 21 2024 09:27:10
%S A365523 1,5,8,8,8,3,0,8,3,3,5,9,6,7,1,8,5,6,5,0,3,3,9,2,7,2,8,7,4,9,0,5,9,4,
%T A365523 0,8,4,5,3,0,0,0,8,0,6,1,6,1,5,3,1,5,2,4,7,2,4,0,8,0,0,5,6,9,6,0,3,6,
%U A365523 1,7,3,1,8,1,8,1,6,8,2,9,3,6,3,5,1,7,9,9,6,1,9,7,8,5,1,2,1,2,5,2,5,2,0,0,8,8,8,6,1,2
%N A365523 Decimal expansion of 6*log(2) - 4.
%C A365523 This sequence is also the decimal expansion of Sum_{k>=1} (-1)^(k+1)*f(k), where f(k) = (4*k^2 - 2*k)/(k^2 + k) is the ratio between the k-th hexagonal and triangular numbers.
%H A365523 Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">A catalog of the real numbers</a> (2011), p. 219.
%H A365523 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.
%H A365523 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A365523 Equals Sum_{k>=1} k/(2^k*(k + 1)*(k + 2)) [Shamos].
%F A365523 Equals Sum_{k>=1} (-1)^(k+1)*(4*k^2 - 2*k)/(k^2 + k).
%e A365523 0.15888308335967185650339272874905940845300080616153...
%t A365523 RealDigits[6*Log[2] - 4, 10 , 100][[1]] (* _Amiram Eldar_, Sep 08 2023 *)
%o A365523 (PARI) 6*log(2)-4
%Y A365523 Cf. A002162. Essentially the same as A016687.
%Y A365523 Cf. A000217, A000384.
%K A365523 nonn,cons
%O A365523 0,2
%A A365523 _Claude H. R. Dequatre_, Sep 08 2023