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

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Last modified June 20 01:36 EDT 2019. Contains 324223 sequences. (Running on oeis4.)