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n^2+n modulo 7.
3

%I #14 Aug 26 2015 10:17:52

%S 0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,

%T 0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,

%U 2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0,0,2,6,5,6,2,0

%N n^2+n modulo 7.

%C Pronic residues (mod m) are analogous to quadratic residues.

%C Periodic with period 7.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 1).

%t Table[Mod[n^2+n,7],{n,0,120}] (* _Harvey P. Dale_, Aug 26 2012 *)

%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 1},{0, 2, 6, 5, 6, 2, 0},105] (* _Ray Chandler_, Aug 26 2015 *)

%o (PARI) A053793(n)=[0, 2, 6, 5, 6, 2, 0][n%7+1] \\ - _M. F. Hasler_, Aug 27 2012

%K nonn,easy

%O 0,2

%A Stuart M. Ellerstein (ellerstein(AT)aol.com), Mar 27 2000

%E More terms from _James A. Sellers_, Apr 08 2000