OFFSET
1,3
COMMENTS
Iwaniec and Friedlander proved there are infinity of the primes of the form i^2+j^4, and hence a(n) increases without bound.
Does not count double representations.
LINKS
John Friedlander and Henryk Iwaniec, Using a parity-sensitive sieve to count prime values of a polynomial, PNAS February 18, 1997 94 (4) 1054-1058.
MATHEMATICA
mx = 2^40; lst = {}; Do[a = i^2 + j^4; If[ PrimeQ[a], AppendTo[lst, a]], {i, Sqrt[mx]}, {j, Sqrt[ Sqrt[mx - i^2]]}]; Table[ Length@ Select[ Union@ lst, # < 2^n &], {n, 40}]
PROG
(PARI) a(n)=my(N=2^n, v=List(), t); for(a=1, sqrt(N), forstep(b=a%2+1, sqrtint(sqrtint(N-a^2)), 2, t=a^2+b^4; if(isprime(t), listput(v, t)))); 1+#vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Jun 12 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Marek Wolf and Robert G. Wilson v, Jun 09 2013
STATUS
approved