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%I #37 Jun 20 2021 02:47:12
%S 5,13,29,41,53,61,73,89,109,113,137,149,157,173,193,229,233,269,281,
%T 293,313,317,349,353,373,389,397,409,433,449,461,509,521,557,569,593,
%U 601,613,617,653,673,701,733,761,773,797,809,853,857,877,929,937,941,953
%N Fouvry-Iwaniec primes: Primes of the form k^2 + p^2 where p is a prime.
%C Sequence is infinite, see Fouvry & Iwaniec.
%C Its intersection with A028916 is A262340, by the uniqueness part of Fermat's two-squares theorem. - _Jonathan Sondow_, Oct 05 2015
%C Named after the French mathematician Étienne Fouvry (b. 1953) and the Polish-American mathematician Henryk Iwaniec (b. 1947). - _Amiram Eldar_, Jun 20 2021
%H Charles R Greathouse IV, <a href="/A185086/b185086.txt">Table of n, a(n) for n = 1..10000</a>
%H Étienne Fouvry and Henryk Iwaniec, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa79/aa7935.pdf">Gaussian primes</a>, Acta Arithmetica, Vol. 79, No. 3 (1997), pp. 249-287.
%H Lasse Grimmelt, <a href="https://arxiv.org/abs/1809.10008">Vinogradov's Theorem with Fouvry-Iwaniec Primes</a>, arXiv:1809.10008 [math.NT], 2018.
%H Art of Problem Solving, <a href="http://www.artofproblemsolving.com/wiki/index.php/Fermat's_Two_Squares_Theorem">Fermat's Two Squares Theorem</a>.
%t nn = 1000; Union[Reap[Do[n = k^2 + p^2; If[n <= nn && PrimeQ[n], Sow[n]], {k, Sqrt[nn]}, {p, Prime[Range[PrimePi[Sqrt[nn]]]]}]][[2, 1]]]
%o (PARI) is(n)=forprime(p=2,sqrtint(n),if(issquare(n-p^2),return(isprime(n))));0
%o (PARI) list(lim)=my(v=List(),N,t);forprime(p=2,sqrt(lim), N=p^2; for(n=1,sqrt(lim-N), if(ispseudoprime(t=N+n^2), listput(v,t)))); v=vecsort(Vec(v),,8); v
%o (Haskell)
%o a185086 n = a185086_list !! (n-1)
%o a185086_list = filter (\p -> any ((== 1) . a010052) $
%o map (p -) $ takeWhile (<= p) a001248_list) a000040_list
%o -- _Reinhard Zumkeller_, Mar 17 2013
%Y Subsequence of A002144 and hence of A002313.
%Y The positive terms of A240130 form a subsequence.
%Y Cf. A010052, A001248, A000040, A028916, A262340.
%K nonn,nice
%O 1,1
%A _Charles R Greathouse IV_, Feb 18 2011