A347952 Decimal expansion of exp(1) * (gamma - Ei(-1)).

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

Offset

1,1

Links

Table of n, a(n) for n=1..110.

M. S. Klamkin, Problem 4946, The American Mathematical Monthly, Vol. 68, No. 1 (1961), p. 67; A Summation, Solutions to Problem 4946 by W. H. M. Kantor and J. W. Wrench, Jr., ibid., Vol. 69, No. 3 (1962), pp. 239-240.

Staff of the Bateman Manuscript Project, Higher Transcendental Functions, Volume II, McGraw-Hill, 1953, p. 143, eq. (5).

Formula

Equals Sum_{k>=1} H(k) / k!, where H(k) is the k-th harmonic number.

Equals -Integral_{x=0..1} exp(x)*log(1-x) dx. - Amiram Eldar, Oct 23 2021

Example

2.16538221532693635942098634849243056838142076774144369...

Mathematica

RealDigits[Exp[1] (EulerGamma - ExpIntegralEi[-1]), 10, 110] [[1]]

Prog

(PARI) exp(1)*(Euler + eint1(1)) \\ Michel Marcus, Oct 24 2021

Crossrefs

Cf. A001008, A001113, A001620, A002805, A073003, A099285, A239069, A244274, A348573.

Sequence in context: A118980 A351385 A090665 * A380351 A376674 A361198

Adjacent sequences: A347949 A347950 A347951 * A347953 A347954 A347955

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Oct 23 2021

Status

approved