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A185086 Fouvry-Iwaniec primes: Primes of the form k^2 + p^2 where p is a prime. 9
5, 13, 29, 41, 53, 61, 73, 89, 109, 113, 137, 149, 157, 173, 193, 229, 233, 269, 281, 293, 313, 317, 349, 353, 373, 389, 397, 409, 433, 449, 461, 509, 521, 557, 569, 593, 601, 613, 617, 653, 673, 701, 733, 761, 773, 797, 809, 853, 857, 877, 929, 937, 941, 953 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence is infinite, see Fouvry & Iwaniec.

Its intersection with A028916 is A262340, by the uniqueness part of Fermat's two-squares theorem. - Jonathan Sondow, Oct 05 2015

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

√Čtienne Fouvry and Henryk Iwaniec, Gaussian primes, Acta Arithmetica 79:3 (1997), pp. 249-287.

Art of Problem Solving, Fermat's Two Squares Theorem

MATHEMATICA

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]]]

PROG

(PARI) is(n)=forprime(p=2, sqrtint(n), if(issquare(n-p^2), return(isprime(n)))); 0

(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

(Haskell)

a185086 n = a185086_list !! (n-1)

a185086_list = filter (\p -> any ((== 1) . a010052) $

               map (p -) $ takeWhile (<= p) a001248_list) a000040_list

-- Reinhard Zumkeller, Mar 17 2013

CROSSREFS

Subsequence of A002144 and hence of A002313.

The positive terms of A240130 form a subsequence.

Cf. A010052, A001248, A000040, A028916, A262340.

Sequence in context: A078598 A155054 A158756 * A277701 A159351 A163251

Adjacent sequences:  A185083 A185084 A185085 * A185087 A185088 A185089

KEYWORD

nonn,nice

AUTHOR

Charles R Greathouse IV, Feb 18 2011

STATUS

approved

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Last modified August 16 23:58 EDT 2018. Contains 313809 sequences. (Running on oeis4.)