A228490 Numbers k for which prime(1) + ... + prime(k) = 2*prime(m) for some m.
3, 7, 55, 59, 65, 75, 93, 133, 137, 141, 249, 277, 313, 365, 375, 387, 391, 435, 471, 499, 563, 573, 597, 605, 619, 645, 675, 719, 787, 797, 799, 815, 825, 845, 867, 879, 919, 937, 957, 971, 1011, 1013, 1145, 1217, 1225, 1243, 1251, 1271, 1283, 1311, 1373
Offset: 1
Keywords
Examples
a(1) = 3 because 2 + 3 + 5 = 2*prime(3) and p(3) = 5 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]/2], 1, 0]; t = Table[p[n], {n, 1, z}]; Flatten[Position[t, 1]]