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

1,2

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

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}]

Crossrefs

Cf. A218858.

Sequence in context: A334584 A054281 A171955 * A210577 A231903 A364405

Adjacent sequences: A225068 A225069 A225070 * A225072 A225073 A225074

Keyword

nonn

Author

T. D. Noe, May 03 2013

Status

approved