%I A122990
%S A122990 8,10,11,16,22,30,34,40,42,47,49,68,74,79,168,202,245,280,463,534
%N A122990 Numbers n such that Sum[ k!, {k,1,n} ]/99 = A007489(n)/99 is prime.
%C A122990 A007489(n) = Sum[ k!, {k,1,n} ] = (!(n+1) - 1) = A003422(n+1) - 1 = {0, 
               1, 3, 9, 33, 153, 873, 5913, 46233, 409113, 4037913, ...}. A007489(n) 
               is divisible by 99 for n=8 and n>9. Corresponding primes of the form 
               (!(n+1) - 1)/99 are {467, 40787, 443987, 225498914387, 11895484822660898387, 
               2771826449193354891007108898387, 3072603482270933019578343003268898387, 
               ...}.
%H A122990 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha132.htm">Factorizations of many number sequences</a>.
%H A122990 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LeftFactorial.html">Left Factorial</a>.
%o A122990 (ARIBAS) f=0;Do[f=f+n!;If[PrimeQ[f/99],Print[{n,f/99}]],{n,1,534}]
%Y A122990 Cf. A007489, A003422 - Left factorial.
%Y A122990 Sequence in context: A031037 A006757 A126803 this_sequence A062372 A046031 
               A102758
%Y A122990 Adjacent sequences: A122987 A122988 A122989 this_sequence A122991 A122992 
               A122993
%K A122990 hard,more,nonn
%O A122990 1,1
%A A122990 Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 28 2006