A079886 Values of x+y where p runs through the primes of form 4k+1 and p=x^2+y^2, 0<=x<=y.

3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 11, 13, 15, 15, 17, 17, 15, 19, 19, 15, 17, 21, 19, 17, 23, 23, 21, 19, 25, 25, 25, 23, 25, 25, 27, 25, 21, 23, 29, 29, 27, 25, 29, 27, 31, 31, 33, 33, 25, 31, 29, 35, 35, 29, 35, 31, 35, 27, 31, 37, 29, 35, 39, 37, 39, 37, 33, 39, 37, 41, 33

Offset: 1

Author

Benoit Cloitre, Jan 13 2003

Keywords

• nonn

Comments

Also values of y where p runs through the primes of form 4k+1 and 2*p=x^2+y^2, 0 Colin Barker, Jul 07 2014

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002330, A002331, A002313, A002144, A079887.

Programs

Maple

N:= 100: # to get values corresponding to primes <= 4*N+1
P:= select(isprime, [seq(4*i+1,i=0..N)]):
F:= proc(p) local f; f:= GaussInt:-GIfactors(p)[2][1][1]; abs(Re(f))+abs(Im(f)) end proc:
map(F,P); # Robert Israel, Jul 07 2014

Mathematica

pp = Select[ Range[200] // Prime, Mod[#, 4] == 1 &]; f[p_] := x + y /. ToRules[ Reduce[0 <= x <= y && p == x^2 + y^2, {x, y}, Integers]]; A079886 = f /@ pp (* Jean-François Alcover, Jan 15 2015 *)