

A306204


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


2



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



OFFSET

1,2


COMMENTS

This is equal to Product_{q>=1} (11/2^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. 3747, 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^i1; 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 A100610
Adjacent sequences: A306201 A306202 A306203 * A306205 A306206 A306207


KEYWORD

nonn,cons


AUTHOR

Tomohiro Yamada, Jan 29 2019


STATUS

approved



