A226496 The number of primes of the form i^2 + j^4 (A028916) <= 2^n, counted with multiplicity.

1, 1, 2, 2, 4, 6, 9, 13, 21, 34, 50, 77, 121, 191, 292, 458, 727, 1164, 1840, 2904, 4650, 7429, 11869, 19087, 30760, 49474, 79971, 129226, 209823, 340347, 552722, 898655, 1461698, 2381041, 3883079, 6338935, 10357549, 16935173, 27712338, 45381521, 51559329

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Counted with double representations. If we do not count doubles, the sequence is A226498.

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, A226495, A226497, A226498.

Programs

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[lst, # <2^n &], {n, 40}]