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A318911 Numbers k such that -3 is a quadratic residue modulo 360*k + 1, 360*k + 2, 360*k + 3 and 360*k + 4.

%I A318911 #18 May 26 2019 19:30:36
%S A318911 0,2,13,17,18,20,21,25,31,40,47,51,54,57,68,69,76,83,91,102,109,110,
%T A318911 117,119,120,131,132,134,138,142,145,149,168,171,174,176,179,182,183,
%U A318911 189,204,205,207,208,211,212,218,229,230,234,245,253,263,281,286,293,295
%N A318911 Numbers k such that -3 is a quadratic residue modulo 360*k + 1, 360*k + 2, 360*k + 3 and 360*k + 4.
%C A318911 Companion sequence to A318527, as it is shown there that all terms in A318527 are congruent to 1 mod 360.
%C A318911 Also numbers k such that -3 is a quadratic residue modulo (360*k + 1)*(360*k + 2)*(360*k + 3)*(360*k + 4)/2.
%C A318911 The number of terms <= 1000, 10000 and 100000 are 156, 1100 and 8056, respectively. There are also 22 pairs of consecutive numbers <= 1000, 99 pairs <= 10000 and 540 pairs <= 100000.
%H A318911 Altug Alkan, <a href="/A318911/b318911.txt">Table of n, a(n) for n = 1..10000</a>
%F A318911 a(n) = (A318527(n) - 1)/360.
%e A318911 2 is a term since 93^2 == -3 (mod 721), 137^2 == -3 (mod 722), 210^2 == -3 (mod 723) and 97^2 == -3 (mod 724).
%o A318911 (PARI) isA057128(n) = issquare(Mod(-3, n));
%o A318911 isA318911(n) = isA057128(360*n+1) && isA057128(360*n+2) && isA057128(360*n+3) && isA057128(360*n+4);
%Y A318911 Cf. A318527.
%K A318911 nonn
%O A318911 1,2
%A A318911 _Jianing Song_, Sep 05 2018