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

1,2

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

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 *)

Crossrefs

Sequence in context: A036864 A058604 A072661 * A334374 A103448 A186904

Adjacent sequences: A103429 A103430 A103431 * A103433 A103434 A103435

Keyword

nonn

Author

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

Extensions

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

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

Status

approved