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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 (list; constant; graph; refs; listen; history; text; internal format)
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: A136369 A305511 A269472 * A007573 A285663 A143909

Adjacent sequences:  A244269 A244270 A244271 * A244273 A244274 A244275

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jun 24 2014

STATUS

approved

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Last modified January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)