%I #5 Oct 02 2013 15:07:14
%S 10,16,18,28,32,34,36,44,46,54,82,136,138,246,250,276,286,362,370,378,
%T 390,554,570,586,588,668,678,684,688,690,726,766,770,826,856,860,878,
%U 880,888,924,928,932,956,962,1048,1160,1174,1210,1264,1286,1292,1506
%N Numbers k for which sum(first k primes) = 3*prime(m) for some m.
%e a(1) = 10 because 2 + 3 + 5 + ... + 29 = 3*prime(14) and p(10) = 29 is the least such prime summand.
%t z = 2800; f[n_] := Sum[Prime[k], {k, 1, n}]; p[n_] := If[PrimeQ[f[n]/3], 1, 0]; t = Table[p[n], {n, 1, z}]; Flatten[Position[t, 1]]
%Y Cf. A013916, A228490.
%K nonn
%O 1,1
%A _Clark Kimberling_, Oct 01 2013
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