A348830 Denominator of relativistic sum w(2n) of the velocities v = 1/p^(2n) over all primes p, in units where the speed of light c = 1.

7, 13, 703, 14527, 524354, 3546333857, 6785975897, 30837755428255, 26315372006162602624, 261082967559450339374, 5060595675665117852243, 39265825923549359199986975497, 123256266165246897346935034271, 2125193947328394509208261354339475, 7291398849693213195350018936947639700634973, 2135676603454582708484868425511295057240283

Offset: 1

Author

Thomas Ordowski, Nov 01 2021

Keywords

• nonn
• frac

Examples

			w(2) = 3/7, w(4) = 1/13, w(6) = 12/703, ...
		

Crossrefs

The numerators are A348829.

Cf. A114362, A114363.

Programs

Mathematica

r[s_] := Zeta[2*s]/Zeta[s]^2; w[s_] := (1 - r[s])/(1 + r[s]); Table[Denominator[w[2*n]], {n, 1, 15}] (* Amiram Eldar, Nov 01 2021 *)

Formula

a(n) = Denominator(tanh(Sum_{p prime} arctanh(1/p^(2n)))).

a(n) = Denominator((zeta(2n)^2-zeta(4n))/(zeta(2n)^2+zeta(4n))).

a(n) = Denominator((1-t(2n))/(1+t(2n))), where t(2n) = A114362(n)/A114363(n).

Extensions

More terms from Amiram Eldar, Nov 01 2021