A079887 Values of y-x where p runs through the primes of form 4k+1 and p=x^2+y^2, 0<=x<=y.

1, 1, 3, 3, 5, 1, 5, 1, 5, 3, 5, 9, 7, 1, 7, 3, 5, 11, 1, 5, 13, 13, 5, 11, 15, 3, 5, 11, 15, 1, 3, 7, 13, 9, 11, 7, 13, 19, 17, 1, 5, 13, 17, 9, 17, 9, 11, 5, 7, 23, 15, 19, 1, 3, 21, 9, 19, 11, 25, 21, 7, 25, 17, 1, 13, 5, 15, 23, 11, 17, 5, 25, 23, 9, 3, 5, 19, 15, 27, 25, 13, 1, 19, 29, 27

Offset: 1

Author

Benoit Cloitre, Jan 13 2003

Keywords

• nonn

Comments

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

Crossrefs

Cf. A002330, A002331, A002313, A002144, A079886.

Programs

Mathematica

pp = Select[ Range[200] // Prime, Mod[#, 4] == 1 &]; f[p_] := y - x /. ToRules[ Reduce[0 <= x <= y && p == x^2 + y^2, {x, y}, Integers]]; A079887 = f /@ pp (* Jean-François Alcover, Jan 15 2015 *)

Formula

a(n) = A002330(n+1)-A002331(n+1). - R. J. Mathar, Jan 09 2017