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 A365522 #20 Jul 14 2025 10:08:00
%S A365522 6,3,8,7,0,4,5,2,8,7,7,9,8,1,8,3,6,5,5,9,7,4,7,6,7,4,6,0,5,1,2,1,6,6,
%T A365522 0,5,7,7,8,3,1,7,2,4,0,1,9,5,1,2,3,6,1,6,3,4,6,7,4,5,9,9,2,0,3,7,5,7,
%U A365522 5,7,5,7,5,9,7,7,7,2,5,9,8,0,3,8,1,2,1,5,3,1,5,8,1,6,5,7,0,5,4,4,0,2,5,1,6,5,6,2,7,0,9,8,6,7,5
%N A365522 Decimal expansion of (Pi*sqrt(3) + 9*log(3))/24.
%C A365522 This sequence is also the decimal expansion of Sum_{k>=1} 1/(f(k) +g(k)), where f(k) and g(k) are respectively the k-th triangular and the 13-gonal numbers (A000217 and A051865).
%H A365522 G. C. Greubel, <a href="/A365522/b365522.txt">Table of n, a(n) for n = 0..10000</a>
%H A365522 Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">A catalog of the real numbers</a> (2011), p. 544.
%H A365522 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.
%F A365522 Equals Sum_{k>=1} 1/(6*k^2 - 4*k) = A244645/2 [Shamos].
%F A365522 Equals - Integral_{x=0..1} log(1-x^6)/x^5 dx [Shamos].
%e A365522 0.63870452877981836559747674605121660577831724019512...
%t A365522 RealDigits[(Pi*Sqrt[3] + 9*Log[3])/24, 10 , 100][[1]] (* _Amiram Eldar_, Sep 08 2023 *)
%o A365522 (PARI) (Pi*sqrt(3)+9*log(3))/24
%o A365522 (Magma) SetDefaultRealField(RealField(139)); R:= RealField(); (Pi(R)*Sqrt(3)+9*Log(3))/24; // _G. C. Greubel_, Mar 24 2024
%o A365522 (SageMath) numerical_approx((pi*sqrt(3)+9*log(3))/24, digits=139) # _G. C. Greubel_, Mar 24 2024
%Y A365522 Cf. A000217, A000796, A002194, A002391, A051865.
%Y A365522 Cf. A244639, A244641, A244645, A244646, A244647, A244648, A244649.
%K A365522 nonn,cons
%O A365522 0,1
%A A365522 _Claude H. R. Dequatre_, Sep 08 2023