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

1,1

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, ..., .

Links

Table of n, a(n) for n=1..12.

Example

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.

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}]

Crossrefs

Cf. A028916, A226496, A226497, A226498.

Sequence in context: A268601 A026577 A204090 * A111643 A000163 A117616

Adjacent sequences: A226492 A226493 A226494 * A226496 A226497 A226498

Keyword

nonn,more

Author

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

Status

approved