A182155 - OEIS

%I #16 Mar 06 2016 12:33:08

%S 0,1,2,6,14,26,66,94,147,264,663,759,916,1089,1213,1343,1554,1706,

%T 2113,2473,2661,2861,3069,3285,3513,3747,3989,4497,4763,5039,5323,

%U 5911,6217,6527,6849,7179,7690,8227,8790,9566,9966,10995,11423,12076,12974,13438

%N Integers of the form: 0/3 + 1/3 + 2/3 + 3/3 + 5/3 + 7/3 + 11/3 + 13/3 + 17/3 + ....

%C Numbers k such that the sum of first n nonnegative noncomposite numbers is equal to 3k.

%H Harvey P. Dale, <a href="/A182155/b182155.txt">Table of n, a(n) for n = 1..1000</a>

%e 1/3 + 2/3 = 1, 1/3 + 2/3 + 3/3 = 2, 1/3 + 2/3 + 3/3 + 5/3 + 7/3 = 6.

%t s = 1; t = {0}; Do[s = s + Prime[n]; If[Mod[s, 3] == 0, AppendTo[t, s/3]], {n, 200}]; t (* _T. D. Noe_, Apr 18 2012 *)

%t Select[Accumulate[Join[{0,1/3},Prime[Range[200]]/3]],IntegerQ] (* _Harvey P. Dale_, Mar 06 2016 *)

%Y Cf. A007504, A154293, A158611.

%K nonn

%O 1,3

%A _Gerasimov Sergey_, Apr 15 2012

%E Definition corrected by _Harvey P. Dale_, Mar 06 2016