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

1,2

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A251260 A022943 A068491 * A239952 A353902 A240076

Adjacent sequences: A364793 A364794 A364795 * A364797 A364798 A364799

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 08 2023

Status

approved