login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A109515
Prime numbers that are the sum of two perfect powers.
1
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
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
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Jul 01 2005
EXTENSIONS
Offset changed to 1 by Robert Israel, Jan 22 2018
STATUS
approved