A330890 Decimal expansion of Product_{prime p == 1 (mod 4)} (1 + 1/p^2)/(1 - 1/p^2).

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, 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, 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

Offset: 1

Author

Vaclav Kotesovec, Apr 30 2020

Keywords

• nonn
• cons

Examples

			1.1136806181323164888618919411983199136565827547877592324456...
		

Crossrefs

Cf. A002144, A088539, A242822, A243380, A242822 (see the second formula).

Cf. A334424/A334425, A334445/A334446, A334449/A334450.

Programs

Mathematica

RealDigits[12*Catalan/Pi^2, 10, 120][[1]]

PARI

12*Catalan/Pi^2 \\ Michel Marcus, May 01 2020

Formula

Equals 12*G/Pi^2, where G is Catalan's constant (A006752).

Equals A243380 / A088539.

Equals Sum_{q in A004613} 2^A001221(q)/q^2. - R. J. Mathar, Jan 27 2021

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

Extensions

Name edited by Thomas Ordowski, Nov 15 2024