OFFSET
1,3
COMMENTS
The condition a >= b >= 0 implies that there is only one Gaussian prime for each norm. - T. D. Noe, Mar 26 2014
The real parts and imaginary parts are listed as a(2n-1) = A300587(n) and a(2n) = A300588(n), respectively. Sequence A239397 lists the pair (y, x) after each pair (x, y), except for (1, 1). - M. F. Hasler, Mar 10 2018
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10106 (5053 pairs)
Eric Weisstein's World of Mathematics, Gaussian prime
Wikipedia, Complex Number
EXAMPLE
From M. F. Hasler, Mar 09 2018: (Start)
Sorted by norm, the smallest Gaussian primes z = x + iy in the first half-quadrant x >= y >= 0 are:
a(1) + i*a(2) = 1 + i;
a(3) + i*a(4) = 2 + i;
a(5) + i*a(6) = 3;
... (End)
MATHEMATICA
mx = 20; lst = Flatten[Table[{a, b}, {a, 0, mx}, {b, 0, a}], 1]; qq = Select[lst, Norm[#] <= mx && PrimeQ[#[[1]] + I*#[[2]], GaussianIntegers -> True] &]; Sort[qq, Norm[#1] < Norm[#2] &]
PROG
(PARI) {for(n=2, 400, f=factor(n*I)/*factor in Z[i]*/; matsize(f)[1]<=2 && vecsum(f[, 2])==2+(f[1, 1]==I) /*either I*p^2 or w*conj(w/I), maybe (1+I)^2 */ && printf("%d, ", vecsort([real(f=f[3-f[1, 2], 1]), imag(f)], , 4)))} \\ For illustrative use. - M. F. Hasler, Mar 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Mar 22 2014
EXTENSIONS
Name changed and in cf. complex -> Gaussian - Wolfdieter Lang, Mar 25 2014
Name edited by M. F. Hasler, Mar 09 2018
STATUS
approved