A048834 Decimal expansion of Sum_{n >= 2} (K(n)/n!), where K(n) is A002034.

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

Offset: 1

Author

Charles T. Le (charlestle(AT)yahoo.com)

Keywords

• nonn
• cons

Comments

This constant was proved to be irrational by Cojocaru and Cojocaru (1996). - Amiram Eldar, Jul 07 2021

Examples

			1.71400629359161602272774384541903375483159792171895...
		

Links

• Charles Ashbacher, Smarandache Sequences, Stereograms and Series, Hexis (2005).
• Ion Cojocaru and Sorin Cojocaru, The Second Constant of Smarandache, Smarandache Notions Journal, Vol. 7, No. 1-2-3 (1996), pp. 119-120.
• Eric Weisstein's World of Mathematics, Smarandache Constants.

Crossrefs

Cf. A002034, A048799.

Programs

Maple

Digits := 80 ; A002034:=[1,2,3,4,5,3,7,4,6,5,11,4,13,7,5,6,17,6,19,5,7,11,23,4,10,13,9,7,29,5,31,8,11,17,7,6,37,19,13,5,41,7,43,11,6,23,47,6,14,10,17,13,53,9,11,7,19,29,59,5,61,31,7,8,13,11,67,17,23,7,71,6,73,37,10,19,11,13,79,6,9,41,83,7]; sma := 0.0 ; for n from 2 to nops(A002034) do sma := sma + A002034[n]/factorial(n) ; od ; # R. J. Mathar, Apr 13 2006

Mathematica

K[n_] := Module[{k = 1}, While[True, If[Divisible[k!, n], Return[k], k++]]];
N[Sum[K[n]/n! , {n, 2, 200}], 103] // RealDigits // First (* Jean-François Alcover, Nov 17 2020 *)

Extensions

More terms from R. J. Mathar, Apr 13 2006

More terms from Jean-François Alcover, Nov 17 2020