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

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, 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, 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

Offset: 1

Author

Artur Jasinski, Dec 28 2020

Keywords

• nonn
• cons

Comments

This is a rational number.

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),

which are rational numbers equal to zeta(4*n)/zeta^2(2*n) = A114362(n+1)/A114363(n+1).

This number has decimal period length 230:

1.25(3617945007235890014471780028943560057887120115774240231548480463096960

9261939218523878437047756874095513748191027496382054992764109985528219

9710564399421128798842257597684515195369030390738060781476121562952243

12590448625180897250).

Examples

			1.25361794500723589001447178...
		

Crossrefs

Cf. A065483, A065484, A065485, A109695, A111003, A114362, A114363, A116393, A167864, A231535, A307868, A330523, A330595, A335319, A335762, A335818, A339925, A340065.

Programs

Mathematica

RealDigits[N[3465/2764, 105]][[1]]

PARI

default(realprecision, 105)
prodeulerrat(1+p^2/((p-1)^2*(p+1)^2),1,3)

Formula

Equals 3465/2764 = 3^2*5*7*11/(2^2*691).

Equals Product_{n>=2} 1+A000040(n)^2/A084920(n)^2.

Equals (9/13)*A340065.