A048799 Decimal expansion of Sum_{n >= 2} 1/S(n)!, where S(n) is the Kempner number A002034(n).

1, 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

By the time n = 100 in the Mathematica coding below, each term < 10^-143.

I conjecture that the constants defined in the present sequence, A048834, A071120, A048835, A048836, A048837, A048838 are irrational. - Sukanto Bhattacharya (susant5au(AT)yahoo.com.au), Apr 28 2008

Examples

			1.09317...
		

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. A071120, A002034, A048834, A038024, A048834, A071120, A048835, A048836, A048837, A048838.

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 (1/S(n)!), where S(n) is the Kempner function A002034 and n >= 2.

Sum (A038024(n)/n!), where A038024(n) = #{k: S(k) = n} and n >= 2. - Jonathan Sondow, Aug 21 2006

Extensions

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