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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
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 (list; constant; graph; refs; listen; history; text; internal format)
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 A226214

Adjacent sequences:  A340063 A340064 A340065 * A340067 A340068 A340069

KEYWORD

nonn,cons

AUTHOR

Artur Jasinski, Dec 28 2020

STATUS

approved

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Last modified May 22 20:52 EDT 2022. Contains 353959 sequences. (Running on oeis4.)