A134653 Number of Gaussian primes a+b*i in the first quadrant (a>0,b>=0) such that n<norm<=1+n.

0, 1, 3, 2, 2, 2, 5, 4, 2, 4, 7, 2, 4, 6, 2, 8, 8, 8, 7, 6, 8, 6, 5, 6, 10, 8, 6, 10, 8, 8, 9, 10, 8, 12, 10, 10, 8, 10, 8, 6, 14, 14, 7, 14, 10, 12, 11, 16, 16, 10, 8, 16, 18, 12, 10, 14, 14, 12, 17, 14, 16

Offset

0,3

Comments

This sequence is different from A055026, which counts the primes according to the exact value of their norm. The present one gives an idea of the variation of the density of Gaussian primes.

Links

Table of n, a(n) for n=0..60.

Example

Examples, written as |a+b*i| = norm (2 decimal digits):
n=0: No prime of norm <=1, so a(0) = 0.
|1+1*i| = 1.41 hence a(1) = 1.
|1+2*i| = |2+1*i| = 2.23, |3+0*i| = 3 hence a(2) = 3.
|1+4*i| = |4+1*i| = 4.12 hence a(3) = 2.

Crossrefs

Cf. A055026.

Sequence in context: A064126 A175333 A130845 * A377320 A090207 A364571

Adjacent sequences: A134650 A134651 A134652 * A134654 A134655 A134656

Keyword

easy,nonn

Author

Philippe Lallouet (philip.lallouet(AT)orange.fr), Jan 31 2008

Extensions

Offset corrected by Jason Yuen, Sep 25 2024

Status

approved