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A071120
Decimal expansion of Sum_{n >= 1} 1/S(n)!, where S(n) is the Kempner number A002034.
2
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
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
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