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A226496 The number of primes of the form i^2 + j^4 (A028916) <= 2^n, counted with multiplicity. 3

%I #14 Aug 18 2015 13:25:48

%S 1,1,2,2,4,6,9,13,21,34,50,77,121,191,292,458,727,1164,1840,2904,4650,

%T 7429,11869,19087,30760,49474,79971,129226,209823,340347,552722,

%U 898655,1461698,2381041,3883079,6338935,10357549,16935173,27712338,45381521,51559329

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

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

%C Counted with double representations. If we do not count doubles, the sequence is A226498.

%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 = 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}]

%Y Cf. A028916, A226495, A226497, A226498.

%K nonn

%O 1,3

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

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)