A225072 Number of first-quadrant Gaussian primes at taxicab distance 2n-1 from the origin.

0, 3, 4, 5, 4, 7, 6, 8, 8, 9, 6, 9, 16, 8, 12, 11, 8, 18, 16, 12, 18, 15, 14, 15, 10, 14, 18, 28, 16, 19, 22, 14, 34, 23, 20, 19, 22, 18, 16, 27, 18, 31, 40, 22, 28, 26, 16, 36, 28, 20, 36, 33, 20, 35, 32, 26, 40, 40, 26, 28, 34, 24, 46, 37, 28, 45, 30, 34, 36

Offset: 1

Author

T. D. Noe, May 03 2013

Keywords

• nonn

Comments

Except for 1+I, 1-I, -1+I, and -1-I, all Gaussian primes are an odd taxicab distance from the origin. Primes on the x- and y-axis are counted only once. That is, although p and p*I are Gaussian primes (for primes p in A002145), we count only p as being a first-quadrant Gaussian prime.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002145, A218858, A225071.

Programs

Mathematica

Table[cnt = 0; Do[If[PrimeQ[n - i + I*i, GaussianIntegers -> True], cnt++], {i, 0, n}]; Do[If[PrimeQ[i - n + I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 0, -1}]; Do[If[PrimeQ[i - n - I*i, GaussianIntegers -> True], cnt++], {i, 1, n}]; Do[If[PrimeQ[n - i - I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 1, -1}]; cnt, {n, 1, 200, 2}]/4