login
A134653
Number of Gaussian primes a+b*i in the first quadrant (a>0,b>=0) such that n<norm<=1+n.
0
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.
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 * A090207 A364571 A202538
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