A250842 - OEIS

%I #10 Dec 16 2019 20:06:31

%S 37,157,1049,7901,16649,78157,615949,1048601,1049201,1064201,1890193,

%T 1953157,1960901,2201957,9915749,17210393,45435449,48860893,60466181,

%U 79235293,79313293,81188293,82382557,130691237,130691357,130769357,205963001,205963601

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

%H Robert Israel, <a href="/A250842/b250842.txt">Table of n, a(n) for n = 1..10000</a>

%e 37 is in this sequence because 37 is prime and 5^1+2^5 = 37.

%e 7901 is in this sequence because 7901 is prime and 5^3+6^5 = 7901.

%p N:= 10^10: # for terms <= N

%p Res:= NULL:

%p for x from 1 to floor(log[5](N)) do

%p   for y from 2 by 2 do

%p      z:= y^5 + 5^x;

%p      if z > N then break fi;

%p      if isprime(z) then Res:= Res, z fi

%p od od:

%p sort([Res]); # _Robert Israel_, Dec 16 2019

%t 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]

%Y Cf. A250546.

%Y Cf. similar sequences listed in A250481.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Nov 29 2014