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

0,1

Comments

This constant is irrational (Sàndor, 1997).

Links

Table of n, a(n) for n=0..86.

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.

Example

0.37213844163204281468199194158558396902073794563977...

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]]

Crossrefs

Cf. A002034, A048834.

Sequence in context: A086313 A016451 A093097 * A086465 A378077 A182502

Adjacent sequences: A343198 A343199 A343200 * A343202 A343203 A343204

Keyword

nonn,cons

Author

Amiram Eldar, Jul 07 2021

Status

approved