cp's OEIS Frontend

A036693 Number of Gaussian integers z = a + bi satisfying n-1 < |z| <= n.

%I A036693 #25 Sep 08 2022 08:44:52
%S A036693 1,4,8,16,20,32,32,36,48,56,64,60,64,88,84,96,88,104,108,120,128,116,
%T A036693 144,136,140,168,160,168,164,176,192,180,208,200,216,228,200,240,220,
%U A036693 264,248,236,264,264,288,284,264,296,292,312
%N A036693 Number of Gaussian integers z = a + bi satisfying n-1 < |z| <= n.
%H A036693 Amiram Eldar, <a href="/A036693/b036693.txt">Table of n, a(n) for n = 0..10000</a>
%H A036693 <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%F A036693 From _Reinhard Zumkeller_, Jan 13 2002: (Start)
%F A036693 a(n)/n ~ 2*Pi.
%F A036693 a(n) = A000328(n)-A000328(n-1). (End)
%e A036693 a(10^2) = 660, a(10^3) = 6392, a(10^4) = 62952, a(10^5) = 628520, a(10^6) = 6281404. - _Reinhard Zumkeller_, Jan 13 2002
%o A036693 (Magma)
%o A036693 [#[<x,y>: x in [-n..n], y in [-n..n]| n-1 lt r and r  le n where r is Sqrt(x^2+ y^2)]: n in [0..50]]; // _Marius A. Burtea_, Feb 18 2020
%o A036693 (Sage)
%o A036693 def A036693(n):
%o A036693     if n == 0: return 1
%o A036693     Range = lambda n: ((i, j) for i in (-n..n) for j in (-n..n))
%o A036693     return sum(1 for (j, k) in Range(n) if (n-1)^2 < j^2 + k^2 <= n^2)
%o A036693 print([A036693(n) for n in range(20)]) # _Peter Luschny_, Mar 27 2020
%Y A036693 Cf. A000328.
%K A036693 nonn
%O A036693 0,2
%A A036693 _Clark Kimberling_