A073685 - OEIS

A073685

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 number of terms in each group.

%I #7 Dec 05 2013 19:55:31

%S 5,3,5,25,2,5,2,2,5,8,6,4,2,3,5,2,2,18,2,35,8,21,2,2,2,6,17,3,6,9,2,8,

%T 11,7,5,15,27,3,4,2,18,3,7,2,2,22,4,12,27,31,2,16,16,5,2,16,2,21,7,12,

%U 2,2,4,22,8,10,2,7,2,2,8,7,8,2,4,22,2,30,8,21,2,3,28,24,4,10,7,4,6,3,2

%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 number of terms in each group.

%t t1 = Rest[Select[Range[970], ! PrimeQ[#] &]]; t = {}; s = c = 0; Do[s += i; c += 1; If[PrimeQ[s], AppendTo[t, c]; s = c = 0], {i, t1}]; t (* _Jayanta Basu_, Jul 07 2013 *)

%Y Cf. A073686, A073687.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Aug 11 2002

%E More terms from _Lior Manor_ Aug 13 2002