%I #8 Jun 24 2014 01:08:25
%S 1,1,2,2,5,1,3,1,2,5,2,6,7,5,3,9,3,2,3,5,2,2,5,1,6,10,13,1,11,8,3,2,3,
%T 1,7,7,18,43,7,6,7,1,27,16,1,7,6,2,1,2,16,6,9,3,2,24,3,1,6,8,6,8,6,19,
%U 6,1,12,5,7,13,1,7,3,7,6,6,1,7,20,20,20,2,1,5,1,10,3,1,7,2,1,13,1,9,9
%N Group the natural numbers so that the product of the terms in each group + 1 is a prime: (1), (2), (3, 4), (5, 6), (7, 8, 9, 10, 11), (12), (13, 14, 15), (16), ... This is the sequence of the number of terms in each group.
%C 4 cannot be a member. Do all other positive integers occur?
%t t = {}; s = 1; c = 0; Do[s = s*i; c += 1; If[PrimeQ[s + 1], AppendTo[t, c]; s = 1; c = 0], {i, 630}]; t (* _Jayanta Basu_, Jul 07 2013 *)
%Y Cf. A073688, A073689.
%K nonn
%O 0,3
%A _Amarnath Murthy_, Aug 12 2002
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 24 2003 and _Dean Hickerson_, Apr 27 2003
