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A239621 Gaussian primes x + i*y, with x = a(2n-1) >= y = a(2n) >= 0, sorted by norm. 5
1, 1, 2, 1, 3, 0, 3, 2, 4, 1, 5, 2, 6, 1, 5, 4, 7, 0, 7, 2, 6, 5, 8, 3, 8, 5, 9, 4, 10, 1, 10, 3, 8, 7, 11, 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, 19, 0 (list; graph; refs; listen; history; text; internal format)
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

Cf. A055025 (norms of Gaussian primes), A239397.

Cf. A300587, A300588.

Sequence in context: A122170 A066029 A141198 * A231204 A180987 A092093

Adjacent sequences:  A239618 A239619 A239620 * A239622 A239623 A239624

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

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Last modified May 22 21:17 EDT 2019. Contains 323504 sequences. (Running on oeis4.)