A103432 - OEIS

%I #20 Feb 26 2019 05:06:12

%S 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,

%T 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,

%U 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

%N 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.

%C Detailed description in A103431.

%H Robert Israel, <a href="/A103432/b103432.txt">Table of n, a(n) for n = 1..10000</a>

%H Sven Simon, <a href="/A103431/a103431_1.txt">List with Gaussian primes of A103431/A103432</a>

%p N:= 100: # to get all terms with norm <= N

%p p1:= select(isprime,[seq(i,i=3..N,4)]):

%p p2:= select(isprime,[seq(i,i=1..N^2,4)]):

%p p2:= map(t -> GaussInt:-GIfactors(t)[2][1][1],p2):

%p p3:= sort( [1+I, op(p1),op(p2)],(a,b) -> Re(a)^2 + Im(a)^2  < Re(b)^2 + Im(b)^2):

%p h:= proc(z)

%p     local a,b;

%p     a:= Re(z); b:= Im(z);

%p     if b = 0 then 0

%p     else

%p       a:= abs(a);

%p       b:= abs(b);

%p       if a = b then a

%p       elif a < b then b,a

%p       else a,b

%p       fi

%p     fi

%p end proc:

%p map(h,p3); # _Robert Israel_, Feb 23 2016

%t maxNorm = 500;

%t norm[z_] := Re[z]^2 + Im[z]^2;

%t m = Sqrt[maxNorm] // Ceiling;

%t gp = Select[Table[a + b I, {a, 1, m}, {b, 0, m}] // Flatten, norm[#] <= maxNorm && PrimeQ[#, GaussianIntegers -> True]&];

%t SortBy[gp, norm[#] maxNorm + Abs[Re[#]]&] // Im (* _Jean-François Alcover_, Feb 26 2019 *)

%K nonn

%O 1,2

%A _Sven Simon_, Feb 05 2005; corrected Feb 20 2005 and again on Aug 06 2006

%E Definition of norm corrected by _Franklin T. Adams-Watters_, Mar 04 2011

%E a(48) corrected by _Robert Israel_, Feb 23 2016