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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. 3

%I #31 Dec 21 2022 22:14:49

%S 7,13,703,14527,524354,3546333857,6785975897,30837755428255,

%T 26315372006162602624,261082967559450339374,5060595675665117852243,

%U 39265825923549359199986975497,123256266165246897346935034271,2125193947328394509208261354339475,7291398849693213195350018936947639700634973,2135676603454582708484868425511295057240283

%N 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.

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

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

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

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

%t 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 *)

%Y The numerators are A348829.

%Y Cf. A114362, A114363.

%K nonn,frac

%O 1,1

%A _Thomas Ordowski_, Nov 01 2021

%E More terms from _Amiram Eldar_, Nov 01 2021

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)