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

%I #14 Sep 25 2024 09:55:18

%S 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,

%T 12,10,10,8,10,8,6,14,14,7,14,10,12,11,16,16,10,8,16,18,12,10,14,14,

%U 12,17,14,16

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

%C 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.

%e Examples, written as |a+b*i| = norm (2 decimal digits):

%e n=0: No prime of norm <=1, so a(0) = 0.

%e |1+1*i| = 1.41 hence a(1) = 1.

%e |1+2*i| = |2+1*i| = 2.23, |3+0*i| = 3 hence a(2) = 3.

%e |1+4*i| = |4+1*i| = 4.12 hence a(3) = 2.

%Y Cf. A055026.

%K easy,nonn

%O 0,3

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

%E Offset corrected by _Jason Yuen_, Sep 25 2024