A250842 Primes of the form 5^x + y^5 with x, y > 0.

37, 157, 1049, 7901, 16649, 78157, 615949, 1048601, 1049201, 1064201, 1890193, 1953157, 1960901, 2201957, 9915749, 17210393, 45435449, 48860893, 60466181, 79235293, 79313293, 81188293, 82382557, 130691237, 130691357, 130769357, 205963001, 205963601

Offset: 1

Author

Vincenzo Librandi, Nov 29 2014

Keywords

• nonn

Examples

			37 is in this sequence because 37 is prime and 5^1+2^5 = 37.
7901 is in this sequence because 7901 is prime and 5^3+6^5 = 7901.
		

Links

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

Crossrefs

Cf. A250546.

Cf. similar sequences listed in A250481.

Programs

Maple

N:= 10^10: # for terms <= N
Res:= NULL:
for x from 1 to floor(log[5](N)) do
  for y from 2 by 2 do
     z:= y^5 + 5^x;
     if z > N then break fi;
     if isprime(z) then Res:= Res, z fi
od od:
sort([Res]); # Robert Israel, Dec 16 2019

Mathematica

f[x_, y_]:= 5^x + y^5; lst={}; Do[p=f[x, y]; If[PrimeQ[p], AppendTo[lst, p]], {y, 50}, {x, 50}]; Take[Union[lst], 50]