%I #12 Apr 08 2024 21:32:10

%S 2,5,13,17,29,31,37,41,43,53,59,61,73,89,97,101,109,113,127,137,149,

%T 157,173,181,193,197,223,229,233,241,251,257,269,277,281,283,293,307,

%U 313,317,337,347,349,353,359,373,379,389,397,401,409,421,433,439,443,449

%N Prime numbers that are the sum of two perfect powers.

%H Robert Israel, <a href="/A109515/b109515.txt">Table of n, a(n) for n = 1..10000</a>

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

%p N:= 1000:

%p PP:= {1, seq(seq(x^k,x=2..floor(N^(1/k))), k=2..ilog2(N))}:

%p A:= select(t -> t<=N and isprime(t), {seq(seq(PP[i]+PP[j],i=1..j),j=1..nops(PP))}):

%p sort(convert(A,list)); # _Robert Israel_, Jan 22 2018

%t 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 *)

%Y Cf. A001597 (perfect powers). Includes A002144.

%K nonn

%O 1,1

%A _Rick L. Shepherd_, Jul 01 2005

%E Offset changed to 1 by _Robert Israel_, Jan 22 2018