%I #29 Feb 16 2025 08:32:52

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

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

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

%N Decimal expansion of second exponential integral at 1, ExpIntegralEi[1].

%D Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 37, table 37:7:1 at page 355.

%H Robert Price, <a href="/A091725/b091725.txt">Table of n, a(n) for n = 1..10000</a>

%H Zbigniew Gołębiewski, Mateusz Klimczak, <a href="https://doi.org/10.1137/1.9781611975505.5">Protection Number of Recursive Trees</a>, 2019 Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FactorialSums.html">Factorial Sums</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>.

%F Equals li(e), where li(x) is the logarithmic integral, and gamma + Sum_{n>=1} 1/(n*n!) = A001620 + A229837. - _Amiram Eldar_, Mar 05 2019

%e 1.89511781635593675546652...

%t RealDigits[ExpIntegralEi[1], 10, 105][[1]] (* _Robert G. Wilson v_, Oct 08 2004 *)

%o (PARI) real(-eint1(-1)) \\ _Charles R Greathouse IV_, Apr 23 2013

%Y Cf. A001563, A001620, A229837.

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_, Feb 01 2004