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A096013 Irregular triangle read by rows: row n lists quadratic nonresidues modulo n.

%I A096013 #31 Feb 16 2025 08:32:53
%S A096013 2,2,3,2,3,2,5,3,5,6,2,3,5,6,7,2,3,5,6,8,2,3,7,8,2,6,7,8,10,2,3,5,6,7,
%T A096013 8,10,11,2,5,6,7,8,11,3,5,6,10,12,13,2,3,5,7,8,11,12,13,14,2,3,5,6,7,
%U A096013 8,10,11,12,13,14,15,3,5,6,7,10,11,12,14,2,3,5,6,8,11,12,14,15,17,2,3,8
%N A096013 Irregular triangle read by rows: row n lists quadratic nonresidues modulo n.
%C A096013 The length of row n is A095972(n).
%H A096013 T. D. Noe, <a href="/A096013/b096013.txt">Rows n = 3..100, flattened</a>
%H A096013 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuadraticNonresidue.html">Quadratic Nonresidue</a>
%e A096013 Triangle starts:
%e A096013   2;
%e A096013   2, 3;
%e A096013   2, 3;
%e A096013   2, 5;
%e A096013   3, 5, 6;
%e A096013   2, 3, 5, 6, 7;
%e A096013   2, 3, 5, 6, 8;
%e A096013   ...
%t A096013 (* As a Triangle *) Table[Complement[Range[n - 1], Mod[Range[n/2]^2, n]], {n, 3, 30}] // Column (* _Mo Li_, Sep 01 2019 *)
%o A096013 (PARI) isA096013(n,m)={local(r);r=1;for(i=0,floor(m/2),if(i^2%m==n,r=0));r} \\ _Michael B. Porter_, May 05 2010
%Y A096013 Cf. A095972.
%K A096013 nonn,tabf
%O A096013 3,1
%A A096013 _Cino Hilliard_, Jul 21 2004
%E A096013 Edited by _Don Reble_, May 07 2006