

A226495


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


3



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


AUTHOR

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


STATUS

approved



