A091131 Decimal expansion of e - 1.

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, 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, 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

Offset: 1

Author

Eric W. Weisstein, Dec 19 2003

Keywords

• nonn
• cons
• easy
• changed

Comments

Average length of the first increasing run in a random permutation of n integers as n->Infinity.

Engel expansion of number e - 1 is sequence of natural numbers (A000027). - Jaroslav Krizek, Jan 23 2014

Examples

			e - 1 = 1.71828182...
		

Links

• Eric Weisstein's World of Mathematics, Permutation
• Index entries for transcendental numbers

Crossrefs

Cf. A001008, A002805.

Essentially the same as A001113.

Programs

Mathematica

RealDigits[N[E - 1, 105]][[1]]

PARI

exp(1) - 1 \\ Michel Marcus, Aug 07 2019

Formula

Sum_{k >= 1} 1/k!. - Eric Desbiaux, Mar 21 2009

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