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

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

Crossrefs

Cf. A088538 (4/Pi), A111003 (Pi^2/8).

Sequence in context: A353160 A011231 A198223 * A138377 A021316 A092092

Adjacent sequences: A331092 A331093 A331094 * A331096 A331097 A331098

Keyword

nonn,cons

Author

Dimitris Valianatos, Jan 08 2020

Status

approved