A159852 n^2 mod 60.

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

Offset: 0

Author

Reinhard Zumkeller, Apr 24 2009

Keywords

• nonn
• easy

Comments

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

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

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

A010421 gives the range of this sequence.

Links

• 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

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

Programs

Mathematica

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 *)
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 *)

PARI

a(n)=n^2%60 \\ Charles R Greathouse IV, May 09 2013