A071120 Decimal expansion of Sum_{n >= 1} 1/S(n)!, where S(n) is the Kempner number A002034.

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

Offset: 1

Author

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

Keywords

• nonn
• cons

Comments

Computed using suggestions from David W. Wilson posted to Sequence Fans mailing list (seqfan(AT)ext.jussieu.fr), May 30 2002

Examples

			2.09317...
		

References

• I. Cojocaru, S. Cojocaru, First Constant of Smarandache, Smarandache Notions Journal, Vol. 7, No. 1-2-3, 1996, 116-118.

Links

• Eric Weisstein's World of Mathematics, Smarandache Constants

Crossrefs

Cf. A048799, A002034, A048834, A038024, A092495.

Programs

Mathematica

f[n_] := DivisorSigma[0, n! ]; s = 1; Do[s = N[s + (f[n + 1] - f[n])/(n + 1)!, 100], {n, 1, 10^4}]; RealDigits[s][[1]]

Formula

Sum_{n>=1} 1/S(n)!, where S(n) is the Kempner function A002034.

Sum_{n>=1} A038024(n)/n!, where A038024(n) = #{k: S(k) = n}. - Jonathan Sondow, Aug 21 2006

Equals 1+A048799.

Extensions

Edited by Robert G. Wilson v and Don Reble, May 30 2002