A070452 a(n) = n^2 mod 30.

0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Equivalently, n^6 mod 30. - Ray Chandler, Dec 27 2023

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1).

Crossrefs

A010462, A070431, A008959, A070435, A070438, A070442, A159852, A000290. - Reinhard Zumkeller, Apr 24 2009

Programs

Mathematica

Table[Mod[n^2,30],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)
LinearRecurrence[{-1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1},{0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9},80] (* Ray Chandler, Aug 26 2015 *)
PowerMod[Range[0,80],6,30] (* or *) PadRight[{},80,{0,1,4,9,16,25,6,19,4,21,10,1,24,19,16,15,16,19,24,1,10,21,4,19,6,25,16,9,4,1}] (* Harvey P. Dale, Jul 10 2023 *)

PARI

a(n)=n^2%30 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[power_mod(n,2,30)for n in range(0, 75)] # Zerinvary Lajos, Nov 03 2009

Formula

From Reinhard Zumkeller, Apr 24 2009: (Start)

a(m*n) = a(m)*a(n) mod 30.

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

a(n+30) = a(n). (End)

a(n)= -a(n-1) +a(n-3) +a(n-4) -a(n-6) -a(n-7) +a(n-9) +a(n-10) -a(n-12) -a(n-13) +a(n-15) +a(n-16) -a(n-18) -a(n-19) +a(n-21) +a(n-22) -a(n-24) -a(n-25) +a(n-27) +a(n-28). - R. J. Mathar, Jul 23 2009