A070441 n^2 mod 19.

0, 1, 4, 9, 16, 6, 17, 11, 7, 5, 5, 7, 11, 17, 6, 16, 9, 4, 1, 0, 1, 4, 9, 16, 6, 17, 11, 7, 5, 5, 7, 11, 17, 6, 16, 9, 4, 1, 0, 1, 4, 9, 16, 6, 17, 11, 7, 5, 5, 7, 11, 17, 6, 16, 9, 4, 1, 0, 1, 4, 9, 16, 6, 17, 11, 7, 5, 5, 7, 11, 17, 6, 16, 9, 4, 1, 0, 1, 4, 9, 16, 6, 17, 11, 7, 5, 5, 7, 11

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

x^2 - k = 19*y, where x, y and k are integers, has solutions if and only if k mod 19 is an element of {0,1,4,5,6,7,9,11,16,17}. - Vincenzo Librandi, Aug 12 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A070442, A070443, A070444.

Programs

Magma

[n^2 mod(19): n in [0..100]]; // Vincenzo Librandi, Aug 12 2014

Maple

A070441:=n->n^2 mod 19: seq(A070441(n), n=0..100); # Wesley Ivan Hurt, Aug 12 2014

Mathematica

Table[Mod[n^2,19],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
PowerMod[Range[0,90],2,19] (* Harvey P. Dale, Mar 23 2012 *)

PARI

a(n)=n^2%19 \\ Charles R Greathouse IV, Apr 06 2016

Formula

a(n+19) = a(n).

a(19*k - n) = a(n). - Robert Israel, Aug 12 2014