cp's OEIS Frontend

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

%I A048799 #19 Feb 16 2025 08:32:40
%S A048799 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,
%T A048799 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 A048799 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 A048799 Decimal expansion of Sum_{n >= 2} 1/S(n)!, where S(n) is the Kempner number A002034(n).
%C A048799 Computed using suggestions from _David W. Wilson_ posted to Sequence Fans mailing list (seqfan(AT)ext.jussieu.fr), May 30 2002
%C A048799 By the time n = 100 in the Mathematica coding below, each term < 10^-143.
%C A048799 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
%D A048799 I. Cojocaru, S. Cojocaru, First Constant of Smarandache, Smarandache Notions Journal, Vol. 7, No. 1-2-3, 1996, 116-118.
%H A048799 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheConstants.html">Smarandache Constants</a>
%F A048799 Sum (1/S(n)!), where S(n) is the Kempner function A002034 and n >= 2.
%F A048799 Sum (A038024(n)/n!), where A038024(n) = #{k: S(k) = n} and n >= 2. - _Jonathan Sondow_, Aug 21 2006
%e A048799 1.09317...
%t A048799 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 A048799 Cf. A071120, A002034, A048834, A038024, A048834, A071120, A048835, A048836, A048837, A048838.
%K A048799 nonn,cons
%O A048799 1,3
%A A048799 Charles T. Le (charlestle(AT)yahoo.com)
%E A048799 Edited by _Robert G. Wilson v_ and _Don Reble_, May 30 2002