

A226496


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


3



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
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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



