cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A070441 n^2 mod 19.

This page as a plain text file.
%I A070441 #37 Dec 18 2023 13:57:43
%S A070441 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,
%T A070441 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,
%U A070441 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
%N A070441 n^2 mod 19.
%C A070441 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
%H A070441 Vincenzo Librandi, <a href="/A070441/b070441.txt">Table of n, a(n) for n = 0..200</a>
%H A070441 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A070441 a(n+19) = a(n).
%F A070441 a(19*k - n) = a(n). - _Robert Israel_, Aug 12 2014
%p A070441 A070441:=n->n^2 mod 19: seq(A070441(n), n=0..100); # _Wesley Ivan Hurt_, Aug 12 2014
%t A070441 Table[Mod[n^2,19],{n,0,200}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 23 2011 *)
%t A070441 PowerMod[Range[0,90],2,19] (* _Harvey P. Dale_, Mar 23 2012 *)
%o A070441 (Magma) [n^2 mod(19): n in [0..100]]; // _Vincenzo Librandi_, Aug 12 2014
%o A070441 (PARI) a(n)=n^2%19 \\ _Charles R Greathouse IV_, Apr 06 2016
%Y A070441 Cf. A070442, A070443, A070444.
%K A070441 nonn,easy
%O A070441 0,3
%A A070441 _N. J. A. Sloane_, May 12 2002