A073687


Group the composite numbers so that the sum of each group is a prime: (4, 6, 8, 9, 10), (12, 14, 15), (16, 18, 20, 21, 22), (24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55), ...; sequence gives first term in each group.


2


%I #7 Dec 05 2013 19:55:31
%S 4,12,16,24,56,58,65,68,70,77,87,94,99,102,106,114,116,118,140,142,
%T 185,195,219,221,224,226,235,255,259,266,278,280,290,302,310,318,334,
%U 366,370,375,377,399,403,411,413,415,442,447,462,494,530,532,550,568,575
%N Group the composite numbers so that the sum of each group is a prime: (4, 6, 8, 9, 10), (12, 14, 15), (16, 18, 20, 21, 22), (24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55), ...; sequence gives first term in each group.
%t t1 = Rest[Select[Range[580], ! PrimeQ[#] &]]; t = {}; s = c = 0; Do[s += i; c += 1; If[PrimeQ[s], AppendTo[t, t1[[Flatten[Position[t1, i]]  c + 1]]]; s = c = 0], {i, t1}]; Flatten[t] (* _Jayanta Basu_, Jul 07 2013 *)
%Y Cf. A073685, A073686.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Aug 11 2002
%E More terms from _Lior Manor_ Aug 13 2002
