

A225072


Number of firstquadrant Gaussian primes at taxicab distance 2n1 from the origin.


2



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
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OFFSET

1,2


COMMENTS

Except for 1+I, 1I, 1+I, and 1I, all Gaussian primes are an odd taxicab distance from the origin. Primes on the x and yaxis 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 firstquadrant Gaussian prime.


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}]/4


CROSSREFS

Cf. A002145, A218858, A225071.
Sequence in context: A232702 A325272 A178698 * A262906 A243607 A242472
Adjacent sequences: A225069 A225070 A225071 * A225073 A225074 A225075


KEYWORD

nonn


AUTHOR

T. D. Noe, May 03 2013


STATUS

approved



