A364796 Numbers k such that the sum of the first k prime powers (not including 1) is a prime power.

1, 2, 3, 6, 8, 13, 18, 20, 22, 37, 41, 43, 46, 62, 87, 89, 95, 99, 111, 115, 118, 124, 130, 146, 150, 160, 164, 168, 180, 192, 201, 205, 211, 221, 263, 283, 287, 315, 339, 352, 356, 364, 396, 398, 408, 418, 434, 442, 450, 476, 508, 512, 526, 534, 536, 548, 556, 582

Offset: 1

Author

Ilya Gutkovskiy, Aug 08 2023

Keywords

• nonn

Examples

			8 is a term because the sum of the first 8 prime powers 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11 = 49 is a prime power.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013916, A013919, A013930, A246655, A364797.

Programs

Mathematica

Position[Accumulate[Select[Range[4000], PrimePowerQ]], _?PrimePowerQ, Heads -> False] // Flatten

PARI

list(lim) = {my(k = 0, s = 0); for(p = 1, lim, if(isprimepower(p), k++; s += p; if(isprimepower(s), print1(k, ", "))));} \\ Amiram Eldar, Jun 20 2025