cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A271586 Number of squares in Z_n[i].

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%I A271586 #13 Aug 03 2018 16:03:00
%S A271586 1,2,5,4,9,10,25,8,37,18,61,20,49,50,45,24,81,74,181,36,125,122,265,
%T A271586 40,121,98,329,100,225,90,481,88,305,162,225,148,361,362,245,72,441,
%U A271586 250,925,244,333,530,1105,120,1177,242,405,196,729,658,549,200,905,450,1741,180,961,962,925,344,441,610,2245
%N A271586 Number of squares in Z_n[i].
%C A271586 Equivalently, the number of distinct pairs (x^2-y^2, 2*x*y) mod n. - _Andrew Howroyd_, Aug 01 2018
%H A271586 Andrew Howroyd, <a href="/A271586/b271586.txt">Table of n, a(n) for n = 1..1000</a>
%e A271586 The squares in Z_3[i] are 0, i, 2i, 1 and 2, therefore a(3)=5.
%t A271586 GG[M_, s_] :=Table[Mod[(a +  b I)^s, M], {a, M}, {b, M}] // Flatten // Union // Length; Table[GG[M, 2], {M, 1, 144}]
%o A271586 (PARI) a(n)={my(v=vector(n)); for(i=0, n-1, for(j=0, n-1, my(k=(i^2-j^2)%n + 1); v[k]=bitor(v[k], 1<<((2*i*j)%n)))); sum(j=1, n, hammingweight(v[j]))} \\ _Andrew Howroyd_, Aug 01 2018
%Y A271586 Cf. A000224.
%K A271586 nonn,mult
%O A271586 1,2
%A A271586 _José María Grau Ribas_, Apr 10 2016
%E A271586 Keyword:mult added by _Andrew Howroyd_, Aug 01 2018