A226495 The number of primes of the form i^2+j^4 (A028916) <= 10^n, counted with multiplicity.

2, 8, 34, 134, 615, 2813, 13415, 65162, 323858, 1626844, 8268241, 42417710

Offset: 1

Author

Marek Wolf and Robert G. Wilson v, Jun 09 2013

Keywords

• nonn
• more

Comments

Iwaniec and Friedlander have proved there is infinity of the primes of the form i^2+j^4.

Primes with more than one representation are counted multiple times.

If we do not count repetitions, the sequence is A226497: 2, 6, 28, 121, 583, 2724, 13175, 64551, ..., .

Examples

			2 = 1^2+1^4, 5 = 2^2+1^4, 17 = 4^2+1^4 = 1^2+2^4, …, 97 = 9^2+2^4 = 4^2+3^4, etc.
		

Crossrefs

Cf. A028916, A226496, A226497, A226498.

Programs

Mathematica

mx = 10^12; 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[lst, # < 10^n &], {n, 12}]