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

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, 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, 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

Offset

3,1

Comments

The length of row n is A095972(n).

Links

T. D. Noe, Rows n = 3..100, flattened

Eric Weisstein's World of Mathematics, Quadratic Nonresidue

Example

Triangle starts:
  2;
  2, 3;
  2, 3;
  2, 5;
  3, 5, 6;
  2, 3, 5, 6, 7;
  2, 3, 5, 6, 8;
  ...

Mathematica

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

Prog

(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

Crossrefs

Cf. A095972.

Sequence in context: A339502 A342821 A165916 * A072380 A144910 A080330

Adjacent sequences: A096010 A096011 A096012 * A096014 A096015 A096016

Keyword

nonn,tabf

Author

Cino Hilliard, Jul 21 2004

Extensions

Edited by Don Reble, May 07 2006

Status

approved