A096013 - OEIS

%I #30 Sep 16 2019 05:21:19

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

%C The length of row n is A095972(n).

%H T. D. Noe, <a href="/A096013/b096013.txt">Rows n = 3..100, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuadraticNonresidue.html">Quadratic Nonresidue</a>

%e Triangle starts:

%e   2;

%e   2, 3;

%e   2, 3;

%e   2, 5;

%e   3, 5, 6;

%e   2, 3, 5, 6, 7;

%e   2, 3, 5, 6, 8;

%e   ...

%t (* As a Triangle *) Table[Complement[Range[n - 1], Mod[Range[n/2]^2, n]], {n, 3, 30}] // Column (* _Mo Li_, Sep 01 2019 *)

%o (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 Cf. A095972.

%K nonn,tabf

%O 3,1

%A _Cino Hilliard_, Jul 21 2004

%E Edited by _Don Reble_, May 07 2006