A103432 Subsequence of the Gaussian primes, where only Gaussian primes a+bi with a>0, b>=0 are listed. Ordered by the norm N(a+bi)=a^2+b^2 and the size of the real part when the norms are equal. The sequence gives the imaginary parts. See A103431 for the real parts.

1, 2, 1, 0, 3, 2, 4, 1, 5, 2, 6, 1, 5, 4, 0, 7, 2, 6, 5, 8, 3, 8, 5, 9, 4, 10, 1, 10, 3, 8, 7, 0, 11, 4, 10, 7, 11, 6, 13, 2, 10, 9, 12, 7, 14, 1, 15, 2, 13, 8, 15, 4, 16, 1, 13, 10, 14, 9, 16, 5, 17, 2, 13, 12, 14, 11, 16, 9, 18, 5, 17, 8, 0, 18, 7, 17, 10, 19, 6, 20, 1, 20, 3, 15, 14, 17

Offset: 1

Author

Sven Simon, Feb 05 2005; corrected Feb 20 2005 and again on Aug 06 2006

Keywords

• nonn

Comments

Detailed description in A103431.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Sven Simon, List with Gaussian primes of A103431/A103432

Programs

Maple

N:= 100: # to get all terms with norm <= N
p1:= select(isprime,[seq(i,i=3..N,4)]):
p2:= select(isprime,[seq(i,i=1..N^2,4)]):
p2:= map(t -> GaussInt:-GIfactors(t)[2][1][1],p2):
p3:= sort( [1+I, op(p1),op(p2)],(a,b) -> Re(a)^2 + Im(a)^2  < Re(b)^2 + Im(b)^2):
h:= proc(z)
    local a,b;
    a:= Re(z); b:= Im(z);
    if b = 0 then 0
    else
      a:= abs(a);
      b:= abs(b);
      if a = b then a
      elif a < b then b,a
      else a,b
      fi
    fi
end proc:
map(h,p3); # Robert Israel, Feb 23 2016

Mathematica

maxNorm = 500;
norm[z_] := Re[z]^2 + Im[z]^2;
m = Sqrt[maxNorm] // Ceiling;
gp = Select[Table[a + b I, {a, 1, m}, {b, 0, m}] // Flatten, norm[#] <= maxNorm && PrimeQ[#, GaussianIntegers -> True]&];
SortBy[gp, norm[#] maxNorm + Abs[Re[#]]&] // Im (* Jean-François Alcover, Feb 26 2019 *)

Extensions

Definition of norm corrected by Franklin T. Adams-Watters, Mar 04 2011

a(48) corrected by Robert Israel, Feb 23 2016