A013919 - OEIS

%I #15 Oct 16 2013 17:44:05

%S 1,2,3,4,6,7,8,9,10,11,12,13,15,16,18,19,21,22,23,24,25,26,27,28,29,

%T 30,31,32,33,34,38,39,40,41,42,44,45,46,49,50,51,52,55,56,57,58,59,60,

%U 61,62,65,66,67,69,70,71,72,76,77,78,79,80,81,82,83,84,85,87,88,89,90,91,92,93

%N Numbers n such that sum of first n composites is composite.

%H Harvey P. Dale, <a href="/A013919/b013919.txt">Table of n, a(n) for n = 1..1000</a>

%t f[ n_Integer ] := Block[ {k = n + PrimePi[ n ] + 1}, While[ k - PrimePi[ k ] - 1 != n, k++ ]; k ]; s = 0; Do[ s = s + f[ n ]; If[ ! PrimeQ[ s ], Print[ n ] ], {n, 1, 100} ]

%t With[{comps=Rest[Select[Range[150],!PrimeQ[#]&]]},Rest[Flatten[ Position[ Accumulate[ comps],_?(!PrimeQ[#]&)]]]] (* _Harvey P. Dale_, Oct 16 2013 *)

%Y Cf. A013920, A013921.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, _Henri Lifchitz_

%E More terms from _David W. Wilson_