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 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 20 13:32 EDT 2022. Contains 353873 sequences. (Running on oeis4.)