A228491 Numbers k for which sum(first k primes) = 3*prime(m) for some m.
10, 16, 18, 28, 32, 34, 36, 44, 46, 54, 82, 136, 138, 246, 250, 276, 286, 362, 370, 378, 390, 554, 570, 586, 588, 668, 678, 684, 688, 690, 726, 766, 770, 826, 856, 860, 878, 880, 888, 924, 928, 932, 956, 962, 1048, 1160, 1174, 1210, 1264, 1286, 1292, 1506
Offset: 1
Keywords
Examples
a(1) = 10 because 2 + 3 + 5 + ... + 29 = 3*prime(14) and p(10) = 29 is the least such prime summand.
Programs
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Mathematica
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]]