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.

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

G. C. Greubel, Table of n, a(n) for n = 1..10000

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

Cf. A000043, A001620, A073004.

Sequence in context: A305511 A269472 A351830 * A007573 A285663 A143909

Adjacent sequences: A244269 A244270 A244271 * A244273 A244274 A244275

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 24 2014

Status

approved