A225071 Number of Gaussian primes at taxicab distance 2n-1 from the origin.

0, 12, 16, 20, 16, 28, 24, 32, 32, 36, 24, 36, 64, 32, 48, 44, 32, 72, 64, 48, 72, 60, 56, 60, 40, 56, 72, 112, 64, 76, 88, 56, 136, 92, 80, 76, 88, 72, 64, 108, 72, 124, 160, 88, 112, 104, 64, 144, 112, 80, 144, 132, 80, 140, 128, 104, 160, 160, 104, 112, 136

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.

Links

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

Crossrefs

Cf. A218858.

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}]