%I #28 Oct 02 2022 23:10:27
%S 1,7,1,8,2,8,1,8,2,8,4,5,9,0,4,5,2,3,5,3,6,0,2,8,7,4,7,1,3,5,2,6,6,2,
%T 4,9,7,7,5,7,2,4,7,0,9,3,6,9,9,9,5,9,5,7,4,9,6,6,9,6,7,6,2,7,7,2,4,0,
%U 7,6,6,3,0,3,5,3,5,4,7,5,9,4,5,7,1,3,8,2,1,7,8,5,2,5,1,6,6,4,2,7,4,2
%N Decimal expansion of e - 1.
%C Average length of the first increasing run in a random permutation of n integers as n->Infinity.
%C Engel expansion of number e - 1 is sequence of natural numbers (A000027). - _Jaroslav Krizek_, Jan 23 2014
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Permutation.html">Permutation</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Sum_{k >= 1} 1/k!. - _Eric Desbiaux_, Mar 21 2009
%F Equals Sum_{k>=1} H(k)*(k-1)/k!, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number. - _Amiram Eldar_, Aug 19 2020
%e e - 1 = 1.71828182...
%t RealDigits[N[E - 1, 105]][[1]]
%o (PARI) exp(1) - 1 \\ _Michel Marcus_, Aug 07 2019
%Y Cf. A001113, A001008, A002805.
%K nonn,cons,easy
%O 1,2
%A _Eric W. Weisstein_, Dec 19 2003