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A226495
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The number of primes of the form i^2+j^4 (A028916) <= 10^n, counted with multiplicity.
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3
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2, 8, 34, 134, 615, 2813, 13415, 65162, 323858, 1626844, 8268241, 42417710
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OFFSET
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1,1
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COMMENTS
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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, ..., .
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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