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

0,3

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).

Formula

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

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

Prog

(Magma) [n^2 mod(19): n in [0..100]]; // Vincenzo Librandi, Aug 12 2014
(PARI) a(n)=n^2%19 \\ Charles R Greathouse IV, Apr 06 2016

Crossrefs

Cf. A070442, A070443, A070444.

Sequence in context: A070442 A086957 A096879 * A070440 A368103 A054580

Adjacent sequences: A070438 A070439 A070440 * A070442 A070443 A070444

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved