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

1,1

Comments

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

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_{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.

Example

2.09317...

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. A048799, A002034, A048834, A038024, A092495.

Sequence in context: A021482 A199287 A198735 * A249417 A189963 A156649

Adjacent sequences: A071117 A071118 A071119 * A071121 A071122 A071123

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