cp's OEIS Frontend

A340066 Decimal expansion of the Product_{p>=3} 1+p^2/((p-1)^2*(p+1)^2) where p are successive prime numbers A000040.

%I A340066 #17 Jan 01 2021 14:34:09
%S A340066 1,2,5,3,6,1,7,9,4,5,0,0,7,2,3,5,8,9,0,0,1,4,4,7,1,7,8,0,0,2,8,9,4,3,
%T A340066 5,6,0,0,5,7,8,8,7,1,2,0,1,1,5,7,7,4,2,4,0,2,3,1,5,4,8,4,8,0,4,6,3,0,
%U A340066 9,6,9,6,0,9,2,6,1,9,3,9,2,1,8,5,2,3,8,7,8,4,3,7,0,4,7,7,5,6,8,7,4,0,9,5,5
%N A340066 Decimal expansion of the Product_{p>=3} 1+p^2/((p-1)^2*(p+1)^2) where p are successive prime numbers A000040.
%C A340066 This is a rational number.
%C A340066 This constant does not belong to the infinite series of prime number products of the form: Product_{p>=2} (p^(2*n)-1)/(p^(2*n)+1),
%C A340066 which are rational numbers equal to zeta(4*n)/zeta^2(2*n) = A114362(n+1)/A114363(n+1).
%C A340066 This number has decimal period length 230:
%C A340066 1.25(3617945007235890014471780028943560057887120115774240231548480463096960
%C A340066 9261939218523878437047756874095513748191027496382054992764109985528219
%C A340066 9710564399421128798842257597684515195369030390738060781476121562952243
%C A340066 12590448625180897250).
%F A340066 Equals 3465/2764 = 3^2*5*7*11/(2^2*691).
%F A340066 Equals Product_{n>=2} 1+A000040(n)^2/A084920(n)^2.
%F A340066 Equals (9/13)*A340065.
%e A340066 1.25361794500723589001447178...
%t A340066 RealDigits[N[3465/2764, 105]][[1]]
%o A340066 (PARI)
%o A340066 default(realprecision, 105)
%o A340066 prodeulerrat(1+p^2/((p-1)^2*(p+1)^2),1,3)
%Y A340066 Cf. A065483, A065484, A065485, A109695, A111003, A114362, A114363, A116393, A167864, A231535, A307868, A330523,  A330595, A335319, A335762, A335818, A339925, A340065.
%K A340066 nonn,cons
%O A340066 1,2
%A A340066 _Artur Jasinski_, Dec 28 2020