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 A330890 #42 Apr 16 2025 05:27:41
%S A330890 1,1,1,3,6,8,0,6,1,8,1,3,2,3,1,6,4,8,8,8,6,1,8,9,1,9,4,1,1,9,8,3,1,9,
%T A330890 9,1,3,6,5,6,5,8,2,7,5,4,7,8,7,7,5,9,2,3,2,4,4,5,6,1,1,5,1,6,3,4,6,7,
%U A330890 5,6,7,2,7,7,2,5,4,6,6,5,1,0,7,5,0,3,6,6,2,7,6,5,2,7,7,4,1,8,1,5,8,8,1,7,2
%N A330890 Decimal expansion of Product_{prime p == 1 (mod 4)} (1 + 1/p^2)/(1 - 1/p^2).
%F A330890 Equals 12*G/Pi^2, where G is Catalan's constant (A006752).
%F A330890 Equals A243380 / A088539.
%F A330890 Equals Sum_{q in A004613} 2^A001221(q)/q^2. - _R. J. Mathar_, Jan 27 2021
%F A330890 Equals (1 + w)/(1 - w), where w = tanh(Sum_{prime p == 1 (mod 4)} arctanh(1/p^2)) = 0.0537832523783875... Physical interpretation: the constant w is the relativistic sum of the velocities c/p^2 over all Pythagorean primes p, in units where the speed of light c = 1. - _Thomas Ordowski_, Nov 14 2024
%e A330890 1.1136806181323164888618919411983199136565827547877592324456...
%t A330890 RealDigits[12*Catalan/Pi^2, 10, 120][[1]]
%o A330890 (PARI) 12*Catalan/Pi^2 \\ _Michel Marcus_, May 01 2020
%Y A330890 Cf. A002144, A088539, A242822, A243380, A242822 (see the second formula).
%Y A330890 Cf. A334424/A334425, A334445/A334446, A334449/A334450.
%K A330890 nonn,cons
%O A330890 1,4
%A A330890 _Vaclav Kotesovec_, Apr 30 2020
%E A330890 Name edited by _Thomas Ordowski_, Nov 15 2024