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A073686
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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 sum of terms in each group.
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3
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%I #7 Dec 05 2013 19:55:31
%S 37,41,97,983,113,307,131,137,367,653,541,383,199,311,547,229,233,
%T 2293,281,5689,1511,4349,439,443,449,1381,4159,769,1571,2441,557,2281,
%U 3253,2137,1567,4877,9439,1103,1487,751,6977,1201,2843,823,827,9413,1777
%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 sum of terms in each group.
%t t1 = Rest[Select[Range[450], ! PrimeQ[#] &]]; t = {}; s = 0; Do[s += i; If[PrimeQ[s], AppendTo[t, s]; s = 0], {i, t1}]; t (* _Jayanta Basu_, Jul 07 2013 *)
%Y Cf. A073685, A073687.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Aug 11 2002
%E More terms from _Lior Manor_ Aug 13 2002
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