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

1,3

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

References

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

Links

Table of n, a(n) for n=1..99.

Eric Weisstein's World of Mathematics, Smarandache Constants

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

Example

1.09317...

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]]

Crossrefs

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

Sequence in context: A085579 A081813 A197003 * A309893 A188887 A378102

Adjacent sequences: A048796 A048797 A048798 * A048800 A048801 A048802

Keyword

nonn,cons

Author

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

Extensions

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

Status

approved