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%I #10 Nov 21 2013 12:49:00
%S 43,89,359,2213,300779,4330763,13997537,36264707,49430879,62570789,
%T 223648559,251239607,393832853,423564767,620650493,746142659,
%U 973242287,1102302953,1160935667,1284365519,1393668629,1784770613,1892819069,3261545603,4306878899
%N Primes of the form p^3 + q^4 where p and q are primes.
%C p and q cannot both be odd. Thus p=2 or q=2. Except for 2^3 + 3^4 = 89, all such primes are of the form 2^4 + q^3.
%F {a(n)} = {p^3 + q^4 in A000040 where p and q are in A000040}.
%e a(1) = 2^4 + 3^3 = 43.
%e a(2) = 2^3 + 3^4 = 89.
%e a(3) = 2^4 + 7^3 = 359.
%e a(4) = 2^4 + 13^3 = 2213.
%e a(5) = 2^4 + 67^3 = 300779.
%e a(6) = 2^4 + 163^3 = 4330763.
%e a(7) = 2^4 + 241^3 = 13997537.
%t upto=45*10^9;With[{c=PrimePi[Ceiling[Power[upto-16, (3)^-1]]]}, Sort[ Join[ {89},Select[#+16&/@(Prime[Range[2,c]]^3),PrimeQ]]]] (* _Harvey P. Dale_, Jul 08 2011 *)
%Y Cf. A000040, A045700 Primes of form p^2+q^3 where p and q are primes.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 21 2006
%E More terms from Harvey P. Dale, Jul 07 2011
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