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A306204 Decimal expansion of Product_{p>=3} (1+1/p) over the Mersenne primes. 3
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} (1-1/2^q)^(-1) over all q with 2^q - 1 a Mersenne prime.
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Tomohiro Yamada, Jan 29 2019
STATUS
approved

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Last modified February 21 08:45 EST 2024. Contains 370228 sequences. (Running on oeis4.)