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

1,2

Comments

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

Links

Table of n, a(n) for n=1..103.

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.

Example

1.71400629359161602272774384541903375483159792171895...

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 *)

Crossrefs

Cf. A002034, A048799.

Sequence in context: A104621 A331900 A176439 * A010504 A242132 A011450

Adjacent sequences: A048831 A048832 A048833 * A048835 A048836 A048837

Keyword

nonn,cons

Author

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

Extensions

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

More terms from Jean-François Alcover, Nov 17 2020

Status

approved