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 A226495 The number of primes of the form i^2+j^4 (A028916) <= 10^n, counted with multiplicity. 3

%I

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

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

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

%C Primes with more than one representation are counted multiple times.

%C If we do not count repetitions, the sequence is A226497: 2, 6, 28, 121, 583, 2724, 13175, 64551, ..., .

%e 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.

%t 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}]

%Y Cf. A028916, A226496, A226497 & A226498.

%K nonn

%O 1,1

%A Marek Wolf) and _Robert G. Wilson v_, Jun 09 2013

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Last modified January 17 18:14 EST 2020. Contains 330987 sequences. (Running on oeis4.)