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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.
11
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.
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
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