A122715 - OEIS

%I #12 Apr 11 2018 18:53:10

%S 521,19687,40353611,27206534396294951,58871586708267917,

%T 977752464192721105849427,1733003264116942402576542827,

%U 24847921085939626319928324473,114264841877247135195655381697

%N Primes of the form p^2 + q^9 where p and q are primes.

%C p and q cannot both be odd. Thus p=2 or q=2. There are no primes of the form 2^9 + q^2 other than 3^2 + 2^9 = 521. Hence all solutions are of the form 2^2 + q^9.

%H Harvey P. Dale, <a href="/A122715/b122715.txt">Table of n, a(n) for n = 1..1000</a>

%F {a(n)} = {p^2 + q^9 in A000040 where p and q are in A000040}.

%e a(1) = 3^2 + 2^9 = 521.

%e a(2) = 2^2 + 3^9 = 19687.

%e a(3) = 2^2 + 7^9 = 40353611.

%e a(4) = 2^2 + 67^9 = 27206534396294951.

%e a(5) = 2^2 + 73^9 = 58871586708267917.

%e a(6) = 2^2 + 453^9 = 803311192691904837821737.

%t s = {521}; Do[ pq = Prime@p^9 + 4; If[ PrimeQ@pq, AppendTo[s, pq]], {p, 300}]; s (* _Robert G. Wilson v_ *)

%t Join[{521},Select[Prime[Range[300]]^9+4,PrimeQ]] (* _Harvey P. Dale_, Apr 11 2018 *)

%Y Cf. A000040, A045700 Primes of form p^2+q^3 where p and q are prime, A122617 Primes of form p^3+q^4 where p and q are primes.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Sep 23 2006

%E More terms from _Robert G. Wilson v_, Sep 26 2006