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n^2 mod 60.
9

%I #10 Jun 19 2018 11:28:44

%S 0,1,4,9,16,25,36,49,4,21,40,1,24,49,16,45,16,49,24,1,40,21,4,49,36,

%T 25,16,9,4,1,0,1,4,9,16,25,36,49,4,21,40,1,24,49,16,45,16,49,24,1,40,

%U 21,4,49,36,25,16,9,4,1,0,1,4,9,16,25,36,49,4,21,40,1,24,49,16,45,16,49,24,1

%N n^2 mod 60.

%C Periodic with period 30: a(n+30) = a(n);

%C a(15*n+k) = a(15*n-k) for k<=15*n;

%C a(m*n) = a(m)*a(n) mod 60;

%C A010421 gives the range of this sequence.

%H <a href="/index/Rec#order_30">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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{0, 1, 4, 9, 16, 25, 36, 49, 4, 21, 40, 1, 24, 49, 16, 45, 16, 49, 24, 1, 40, 21, 4, 49, 36, 25, 16, 9, 4, 1},80] (* _Ray Chandler_, Aug 26 2015 *)

%t PowerMod[Range[0,80],2,60] (* or *) PadRight[{},80,{0,1,4,9,16,25,36,49,4,21,40,1,24,49,16,45,16,49,24,1,40,21,4,49,36,25,16,9,4,1}] (* _Harvey P. Dale_, Jun 19 2018 *)

%o (PARI) a(n)=n^2%60 \\ _Charles R Greathouse IV_, May 09 2013

%Y Cf. A070431, A008959, A070435, A070438, A070442, A070452, A000290.

%K nonn,easy

%O 0,3

%A _Reinhard Zumkeller_, Apr 24 2009