|
%I #31 Mar 27 2018 17:21:17
%S 1,1,0,2,1,2,1,4,0,2,5,3,5,4,1,3,7,0,4,7,6,2,9,7,1,2,8,4,1,10,9,5,2,
%T 12,11,9,5,8,0,7,10,6,1,3,14,12,7,4,10,5,11,0,10,14,13,1,8,5,17,16,4,
%U 13,6,12,1,5,15,2,9,19,12,17,11,5,14,10,18,4,6,16,20,19,10,13,0,4,6
%N Imaginary part y of the n-th Gaussian prime x + i*y, x >= y >= 0, ordered by norm x^2 + y^2 = A055025(n)^2.
%C With the restriction Re(z) >= Im(z) >= 0 used here and in A239621, there is exactly one Gaussian prime z for each possible norm |z|^2 in A055025. Sequence A239397 lists both, (x, y) and (y, x), for each of these having x > y (i.e., except for x = y = 1).
%C According to the graph, the values seem rather uniformly distributed between 0 and the upper bound sqrt(A055025(n)/2) ~ sqrt(n log n), in contrast to the values of the real parts A300587(n).
%H M. F. Hasler, <a href="/A300588/b300588.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A239621(2n) = A239397(4n-3) (= A239397(4n-4) for n > 1).
%F a(n) = sqrt(A055025(n) - A300587(n)^2).
%e The smallest Gaussian primes with Re(z) >= Im(z) >= 0, ordered by norm, are 1+i, 2+i, 3, 3+i, ...
%e Their imaginary parts, listed here, are a(1) = 1, a(2) = 1, a(3) = 0, a(4) = 1,
%o (PARI) c=1; for(n=1,oo, matsize(f=factor(n*I))[1]<=2 && vecsum(f[,2])==2+(f[1, 1]==I) && !write("/tmp/b300588.txt",c" "min(real(f=f[3-f[1,2],1]),imag(f))) && c++>1e4 && break) \\ Replace write("/tmp/b300588.txt",c" by print1(" to print the values.
%Y Even bisection of A239621. See A300587 for real parts, A055025 for the norms.
%K nonn
%O 1,4
%A _M. F. Hasler_, Mar 09 2018
|
