A331095 - OEIS

A331095

Decimal expansion of 32/Pi^3.

1, 0, 3, 2, 0, 4, 9, 1, 0, 1, 8, 6, 2, 3, 8, 3, 6, 5, 3, 9, 0, 1, 5, 0, 5, 6, 8, 6, 0, 3, 4, 0, 3, 8, 0, 3, 4, 9, 7, 8, 0, 2, 6, 7, 5, 6, 7, 1, 9, 2, 9, 8, 4, 5, 5, 5, 0, 6, 6, 1, 5, 1, 1, 0, 8, 9, 8, 6, 8, 9, 9, 7, 7, 4, 2, 3, 8, 5, 5, 6, 6, 5, 2, 2, 3, 2, 1, 3, 2, 7, 3, 9, 0, 6, 0, 9, 6

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OFFSET

1,3

COMMENTS

For odd prime numbers: Product_{odd primes p} 1/(1 - 1/p^2) = Pi^2/8 = (3/4)*zeta(2) = A111003.

For odd composite numbers: Product_{odd composite numbers c} 1/(1 - 1/c^2) = (81/80) * (225/224) * (441/440) * (625/624) * (729/728) * ... = 32/Pi^3, this constant.

LINKS

Table of n, a(n) for n=1..97.

Index entries for transcendental numbers

FORMULA

Equals A088538/A111003.

EXAMPLE

1.032049101862383653901505686034038...

MATHEMATICA

RealDigits[32/Pi^3, 10, 100][[1]] (* Amiram Eldar, Jan 10 2020 *)

PROG

(PARI) p = 1.0; forstep(n = 3, 10^7, 2, if(!isprime(n), p*= (1 / (1 - 1 / n^2)))); print(p)

(PARI) 32/Pi^3