A070446 a(n) = n^2 mod 24.

0, 1, 4, 9, 16, 1, 12, 1, 16, 9, 4, 1, 0, 1, 4, 9, 16, 1, 12, 1, 16, 9, 4, 1, 0, 1, 4, 9, 16, 1, 12, 1, 16, 9, 4, 1, 0, 1, 4, 9, 16, 1, 12, 1, 16, 9, 4, 1, 0, 1, 4, 9, 16, 1, 12, 1, 16, 9, 4, 1, 0, 1, 4, 9, 16, 1, 12, 1, 16, 9, 4, 1, 0, 1, 4, 9, 16, 1, 12, 1, 16, 9, 4, 1, 0, 1, 4, 9, 16, 1, 12, 1

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Periodic with period = 12. - Harvey P. Dale, Jun 19 2014

From Jesse Fiedler, Aug 23 2019: (Start)

If a(n) = 1, then n is odd and is not divisible by 3.

For n <= 7919 and a(n)=1, approximately 37.8% of values of n are prime.

For n <= 104729, and a(n)=1, approximately 28.64% of values of n are prime.

(End)

Links

• 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, 1).

Programs

Mathematica

Table[Mod[n^2,24],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
PowerMod[Range[0,100],2,24] (* or *) PadRight[{},100,{0,1,4,9,16,1,12,1,16,9,4,1}] (* Harvey P. Dale, Jun 19 2014 *)

PARI

a(n)=n^2%24 \\ Charles R Greathouse IV, Apr 06 2016