A340066 - OEIS

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

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OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..105.

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.

EXAMPLE

1.25361794500723589001447178...

MATHEMATICA

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

PROG

(PARI)

default(realprecision, 105)

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

CROSSREFS

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

Sequence in context: A085825 A198140 A339259 * A212614 A037852 A367433

Adjacent sequences: A340063 A340064 A340065 * A340067 A340068 A340069

KEYWORD

nonn,cons

AUTHOR

Artur Jasinski, Dec 28 2020

STATUS

approved