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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), ... Sequence gives first term in each group.
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%I #6 Dec 05 2013 19:55:31

%S 1,2,3,5,7,12,13,16,17,19,24,26,32,39,44,47,56,59,61,64,69,71,73,78,

%T 79,85,95,108,109,120,128,131,133,136,137,144,151,169,212,219,225,232,

%U 233,260,276,277,284,290,292,293,295,311,317,326,329,331,355,358,359,365

%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), ... Sequence gives first term in each group.

%C a(k+1) - a(k) = 4 has no solution.

%t t = {}; s = 1; c = 0; Do[s = s*i; c += 1; If[PrimeQ[s + 1], AppendTo[t, i - c + 1]; s = 1; c = 0], {i, 375}]; t (* _Jayanta Basu_, Jul 07 2013 *)

%Y Cf. A073688, A073690.

%K nonn

%O 0,2

%A _Amarnath Murthy_, Aug 12 2002

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 24 2003