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A244272
Decimal expansion of exp(gamma)/log(2), a conjectural constant related to the asymptotic counting of Mersenne primes, where gamma is Euler's constant.
1
2, 5, 6, 9, 5, 4, 4, 3, 4, 4, 8, 9, 8, 5, 7, 3, 6, 0, 7, 3, 7, 0, 0, 4, 4, 1, 1, 1, 9, 3, 9, 1, 4, 5, 6, 1, 6, 9, 8, 8, 8, 5, 8, 3, 9, 6, 7, 2, 6, 0, 9, 5, 6, 0, 3, 8, 4, 2, 0, 7, 7, 9, 6, 4, 2, 2, 5, 2, 8, 5, 3, 4, 1, 2, 9, 1, 8, 3, 5, 2, 9, 9, 8, 9, 4, 9, 4, 6, 9, 4, 0, 4, 5, 6, 9, 6, 7, 4, 9, 3, 6, 9, 6
OFFSET
1,1
COMMENTS
Let M(n) denote the number of primes p <= n, for which 2^p-1 is prime. It is conjectured that M(n) -> infinity and that M(n) ~ exp(gamma)/log(2)*log(n).
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.5 Euler-Mascheroni Constant, p. 29.
LINKS
Eric Weisstein's MathWorld, Mersenne Prime
EXAMPLE
2.569544344898573607370044111939...
MATHEMATICA
RealDigits[Exp[EulerGamma]/Log[2], 10, 103] // First
PROG
(PARI) default(realprecision, 100); exp(Euler)/log(2) \\ G. C. Greubel, Sep 06 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(EulerGamma(R))/Log(2); // G. C. Greubel, Sep 06 2018
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved