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 A255933 a(n) is the largest integer m such that s/(m!-1) is integer, where s is the sum of all previous terms; a(1)=1. 0
 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 4, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 5, 2, 2, 2, 3, 2, 3, 4, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 2, 2, 5, 2, 3, 2, 3, 4, 2, 2, 2, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For all n>1, a(n) exists and is at least 2, since 2 gives a denominator (2!-1) = 1, thus an integer. The sequence of partial sums is: 1,3,5,8,10,13,15,18,20,23,27,29,31,33,35,38,... The record values occur at n=1,2,4,11,49,286,1997,... LINKS MAPLE a(5) = 2 since (1+2+2+3)/(n!-1) = 8/(2!-1) = 8, an integer. a(6) = 3 since (1+2+2+3+2)/(n!-1) = 10/(3!-1) = 2, an integer. PROG (PARI) lista(nn) = {v = [1]; s = 1; print1(s, ", "); for (n=2, nn, k = 2; while(k!-1 <= s, k++); until (type(s/(k!-1)) == "t_INT", k--); s += k; print1(k, ", "); v = concat(v, k); ); } \\ Michel Marcus, Mar 11 2015 CROSSREFS Sequence in context: A163178 A219545 A029374 * A319396 A049237 A162361 Adjacent sequences:  A255930 A255931 A255932 * A255934 A255935 A255936 KEYWORD nonn AUTHOR Neri Gionata, Mar 11 2015 STATUS approved

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Last modified April 25 00:29 EDT 2019. Contains 322446 sequences. (Running on oeis4.)