A306770 Decimal expansion of Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!).
4, 0, 0, 3, 7, 9, 6, 7, 7, 0, 0, 4, 6, 4, 1, 3, 4, 0, 5, 0, 0, 2, 7, 8, 6, 2, 7, 1, 0, 3, 4, 3, 0, 6, 5, 9, 7, 8, 2, 3, 4, 5, 8, 4, 7, 9, 0, 7, 1, 7, 5, 5, 8, 2, 1, 2, 6, 5, 0, 6, 4, 3, 0, 7, 2, 6, 4, 3, 0, 5, 2, 2, 5, 9, 7, 4, 0, 8, 1, 1, 1, 9, 5, 9, 4, 2, 8, 5, 3, 1
Offset: 0
Examples
0.40037967700464134050027...
Links
- Eric Weisstein's World of Mathematics, Exponential Integral.
Programs
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PARI
exp(1) - 1 + Euler - real(-eint1(-1)) \\ Michel Marcus, Mar 09 2019
Formula
Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!) = exp(1) - 1 + gamma - ExpIntegralEi[1].
From Amiram Eldar, Jun 26 2021: (Start)
Equals Sum_{k>=2} 1/A054119(k).
Equals -Integral{x=0..1} x*log(x)*exp(x) dx. (End)