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 A365524 #19 Mar 28 2025 02:10:40
%S A365524 2,7,2,5,8,8,7,2,2,2,3,9,7,8,1,2,3,7,6,6,8,9,2,8,4,8,5,8,3,2,7,0,6,2,
%T A365524 7,2,3,0,2,0,0,0,5,3,7,4,4,1,0,2,1,0,1,6,4,8,2,7,2,0,0,3,7,9,7,3,5,7,
%U A365524 4,4,8,7,8,7,8,7,7,8,8,6,2,4,2,3,4,5,3,3,0,7,9,8,5,6,7,4,7,5,0,1,6,8,0,0,5,9,2,4,0,8
%N A365524 Decimal expansion of 4*log(2) - 5/2.
%C A365524 This sequence is also the decimal expansion of Sum_{k>=1} (-1)^(k+1)*f(k), where f(k) = (3*k^2 - k)/(k^2 + k) is the ratio between the k-th pentagonal and triangular numbers.
%H A365524 Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">A catalog of the real numbers</a> (2011), p. 330.
%H A365524 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.
%H A365524 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A365524 Equals Sum_{k>=1} 1/(2^k*(k + 2)) [Shamos].
%F A365524 Equals Sum_{k>=1} (-1)^(k+1)*(3*k^2 - k)/(k^2 + k).
%e A365524 0.27258872223978123766892848583270627230200053744102...
%t A365524 RealDigits[4*Log[2] - 5/2, 10 , 100][[1]] (* _Amiram Eldar_, Sep 08 2023 *)
%o A365524 (PARI) 4*log(2)-5/2
%Y A365524 Cf. A002162.
%Y A365524 Cf. A000217, A000326, A358517.
%Y A365524 Essentially the same as A016639 and A358517.
%K A365524 nonn,cons
%O A365524 0,1
%A A365524 _Claude H. R. Dequatre_, Sep 08 2023