A247377 Decimal expansion of Integral_{0..oo} 1/Gamma(1+x) dx, a variation of the Fransén-Robinson constant.

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 4.6 Fransén-Robinson constant, p. 263.

Links

Table of n, a(n) for n=1..104.

Eric Weisstein's MathWorld, Fransén-Robinson Constant

Formula

Also equals e - Integral_{-oo..oo} e^(-e^x)/(x^2 + Pi^2) dx (observed by Ramanujan).

Example

2.266534507699848835071963857678220918408829714280222193861...

Mathematica

NIntegrate[1/Gamma[1 + x], {x, 0, Infinity}, WorkingPrecision -> 104] // RealDigits // First

Prog

(Python)
from mpmath import *
mp.dps = 200
A247377 = [d for d in nstr(quad(lambda x:1/gamma(1+x), [0, inf]), n=mp.dps)[:-1] if d != '.'] # Chai Wah Wu, Sep 16 2014
(PARI)
localprec(100); intnum(x=0, [[1], 1], 1/gamma(1+x)) \\ Dumitru Damian, Oct 12 2023

Crossrefs

Cf. A058655.

Sequence in context: A171661 A276418 A173869 * A167909 A368745 A185421

Adjacent sequences: A247374 A247375 A247376 * A247378 A247379 A247380

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 15 2014

Status

approved