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
Examples
2.1018939453352041890527971856880849019959920074584239...
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.
Programs
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Magma
SetDefaultRealField(RealField(100)); R:= RealField(); 1/(2^(Exp(-EulerGamma(R))) - 1); // G. C. Greubel, Sep 04 2018
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Mathematica
c = 1/(2^(E^(-EulerGamma)) - 1); RealDigits[c, 10, 99] // First
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PARI
1/(2^(exp(-Euler))-1) \\ Michel Marcus, Sep 25 2014
Formula
c = 1/(2^(e^(-gamma))-1), where gamma is Euler's constant 0.5772...