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

%I #19 Apr 22 2024 06:25:31

%S 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,

%T 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,

%U 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

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

%C Computed using suggestions from _David W. Wilson_ posted to Sequence Fans mailing list (seqfan(AT)ext.jussieu.fr), May 30 2002

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmarandacheConstants.html">Smarandache Constants</a>

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

%F Sum_{n>=1} A038024(n)/n!, where A038024(n) = #{k: S(k) = n}. - _Jonathan Sondow_, Aug 21 2006

%F Equals 1+A048799.

%e 2.09317...

%t 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]]

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

%K nonn,cons

%O 1,1

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

%E Edited by _Robert G. Wilson v_ and _Don Reble_, May 30 2002