A109515 Prime numbers that are the sum of two perfect powers.

2, 5, 13, 17, 29, 31, 37, 41, 43, 53, 59, 61, 73, 89, 97, 101, 109, 113, 127, 137, 149, 157, 173, 181, 193, 197, 223, 229, 233, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 337, 347, 349, 353, 359, 373, 379, 389, 397, 401, 409, 421, 433, 439, 443, 449

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The prime 17 is a term because 17 = 2^3 + 3^2.

Maple

N:= 1000:
PP:= {1, seq(seq(x^k, x=2..floor(N^(1/k))), k=2..ilog2(N))}:
A:= select(t -> t<=N and isprime(t), {seq(seq(PP[i]+PP[j], i=1..j), j=1..nops(PP))}):
sort(convert(A, list)); # Robert Israel, Jan 22 2018

Mathematica

lim=450; Select[Union[Total/@Permutations[Flatten[Table[Union[Select[Range[2, lim], ResourceFunction["PerfectPowerQ"][#]&], {1}], 2]], {2}]], PrimeQ[#]&&#<lim&] (* James C. McMahon, Apr 08 2024 *)

Crossrefs

Cf. A001597 (perfect powers). Includes A002144.

Sequence in context: A019362 A317964 A075451 * A135933 A086807 A002313

Adjacent sequences: A109512 A109513 A109514 * A109516 A109517 A109518

Keyword

nonn

Author

Rick L. Shepherd, Jul 01 2005

Extensions

Offset changed to 1 by Robert Israel, Jan 22 2018

Status

approved