A343201 Decimal expansion of Sum_{n>=1} (-1)^(n+1)*K(n)/n!, where K(n) is the Kempner function (A002034).

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

Offset: 0

Author

Amiram Eldar, Jul 07 2021

Keywords

• nonn
• cons

Comments

This constant is irrational (Sàndor, 1997).

Examples

			0.37213844163204281468199194158558396902073794563977...
		

Links

• József Sàndor, On the irrationality of certain alternative Smarandache series, in: C. Dumitrescu and V. Seleacu (eds.), Proceedings of the first international conference on Smarandache type notions in number theory, University of Craiova, 21-24 August 1997, American Research Press, 1997, pp. 124-125.

Crossrefs

Cf. A002034, A048834.

Programs

Mathematica

kempner[n_] := Module[{k = 1}, While[! Divisible[k!, n], k++]; k]; RealDigits[Sum[(-1)^(n + 1) * kempner[n]/n!, {n, 1, 100}], 10, 100][[1]]