A247864 Decimal expansion of c = 1/(2^(e^(-gamma))-1), a constant associated with the asymptotic convergent denominators of a continued fraction using Mersenne primes.

2, 1, 0, 1, 8, 9, 3, 9, 4, 5, 3, 3, 5, 2, 0, 4, 1, 8, 9, 0, 5, 2, 7, 9, 7, 1, 8, 5, 6, 8, 8, 0, 8, 4, 9, 0, 1, 9, 9, 5, 9, 9, 2, 0, 0, 7, 4, 5, 8, 4, 2, 3, 9, 0, 6, 5, 8, 8, 0, 0, 3, 7, 2, 9, 5, 5, 2, 9, 7, 8, 9, 5, 7, 2, 2, 8, 3, 4, 5, 6, 7, 8, 0, 5, 4, 6, 0, 8, 0, 2, 2, 5, 4, 4, 3, 2, 4, 0, 3

Offset

1,1

Links

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

Eric Weisstein's MathWorld, Mersenne Prime

Marek Wolf, "Continued fractions constructed from prime numbers" arXiv:1003.4015 [math.NT] Sep 26 2010, p. 24.

Formula

c = 1/(2^(e^(-gamma))-1), where gamma is Euler's constant 0.5772...

Example

2.1018939453352041890527971856880849019959920074584239...

Mathematica

c = 1/(2^(E^(-EulerGamma)) - 1); RealDigits[c, 10, 99] // First

Prog

(PARI) 1/(2^(exp(-Euler))-1) \\ Michel Marcus, Sep 25 2014
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 1/(2^(Exp(-EulerGamma(R))) - 1); // G. C. Greubel, Sep 04 2018

Crossrefs

Cf. A000668, A001620.

Sequence in context: A085324 A264945 A326476 * A370398 A331278 A266632

Adjacent sequences: A247861 A247862 A247863 * A247865 A247866 A247867

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 25 2014

Status

approved