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

1,3

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.

Links

Table of n, a(n) for n=1..41.

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 = 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}]

Crossrefs

Cf. A028916, A226495, A226497, A226498.

Sequence in context: A209603 A192684 A274147 * A047084 A058518 A018139

Adjacent sequences: A226493 A226494 A226495 * A226497 A226498 A226499

Keyword

nonn

Author

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

Status

approved