A070442 -id:A070442 - cp's OEIS frontend

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

N. J. A. Sloane, May 12 2002

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

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).

Cf. A070442, A070443, A070444.

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

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

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 *)

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

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

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

A070440 a(n) = n^2 mod 18.

Original entry on oeis.org

0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9, 4, 1, 0, 1, 4, 9, 16, 7, 0, 13, 10, 9, 10, 13, 0, 7, 16, 9

Offset: 0

N. J. A. Sloane, May 12 2002

G. C. Greubel, Table of n, a(n) for n = 0..1000
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, 1).

Cf. A070441, A070442.

Table[Mod[n^2,18],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)

a(n)=n^2%18 \\ Charles R Greathouse IV, Apr 06 2016

a(n) = a(n-18). - R. J. Mathar, Jul 27 2015

G.f.: -x*(1 +4*x +9*x^2 +16*x^3 +7*x^4 +13*x^6 +10*x^7 +9*x^8 +10*x^9 +13*x^10 +7*x^12 +16*x^13 +9*x^14 +4*x^15 +x^16) / ( (x-1)*(1+x+x^2)*(1+x^3+x^6)*(1+x)*(1-x+x^2)*(1-x^3+x^6) ). - R. J. Mathar, Jul 27 2015

cp's OEIS Frontend

A070441 n^2 mod 19.

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