A182288 Primes of form a^2+b^2 such that |a|+|b| is prime of the form 4k+3.

5, 29, 37, 61, 73, 101, 181, 193, 241, 269, 277, 293, 349, 409, 521, 541, 593, 661, 701, 929, 937, 1009, 1069, 1109, 1117, 1129, 1217, 1237, 1249, 1289, 1609, 1741, 1753, 1789, 1801, 2029, 2053, 2161, 2221, 2269, 2357, 2389, 2521, 2557, 2609, 2633, 2741, 2753

Offset: 1

Author

Thomas Ordowski, Apr 23 2012

Keywords

• nonn

Examples

			The prime 29=5^2+2^2 such that 5+2=7 is prime of form 4k+3.
		

Links

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

Crossrefs

Cf. A099332.

Programs

Mathematica

nn = 60; t = {}; Do[p1 = a^2 + b^2; p2 = a + b; If[p1 < nn^2 && PrimeQ[p1] && Mod[p2, 4] == 3 && PrimeQ[p2], AppendTo[t, p1]], {a, nn}, {b, a}]; Sort[t] (* T. D. Noe, Apr 23 2012 *)

PARI

list(lim)=my(v=List(),t);for(a=1,sqrt(lim),forstep(b=(2-a)%4+1, min(a,sqrt(lim-a^2)),4,if(isprime(a+b)&&isprime(t=a^2+b^2), listput(v,t)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Apr 24 2012

Extensions

Extended by T. D. Noe, Apr 23 2012