A306204 Decimal expansion of Product_{p>=3} (1+1/p) over the Mersenne primes.

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

Offset

1,2

Comments

This is equal to Product_{q>=1} (1-1/2^q)^(-1) over all q with 2^q - 1 a Mersenne prime.

Links

Tomohiro Yamada, Table of n, a(n) for n = 1..99

Tomohiro Yamada, Unitary super perfect numbers, Mathematica Pannonica, Volume 19, No. 1, 2008, pp. 37-47, using this constant with only a rough upper bound (4/3)*exp(4/21) < 1.6131008.

Formula

Equals Sum_{n>=1} 1/A046528(n). - Amiram Eldar, Jan 06 2021

Example

Decimal expansion of (4/3) * (8/7) * (32/31) * (128/127) * (8192/8191) * (131072/131071) * (524288/524287) * ... = 1.585558887...

Prog

(PARI) t=1.0; for(i=1, 500, p=2^i-1; if(isprime(p), t=t*(p+1)/p))

Crossrefs

Cf. A065446 (the corresponding product over all Mersenne numbers, prime or composite).

Cf. A173898 (the sum of reciprocals of the Mersenne primes).

Cf. A065442 (the sum of reciprocals of the Mersenne numbers, prime or composite).

Cf. A046528.

Sequence in context: A090550 A171819 A171541 * A178331 A199395 A366163

Adjacent sequences: A306201 A306202 A306203 * A306205 A306206 A306207

Keyword

nonn,cons

Author

Tomohiro Yamada, Jan 29 2019

Status

approved