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

0,3

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).

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

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 *)

Prog

(Sage) [power_mod(n, 2, 30)for n in range(0, 75)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=n^2%30 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

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

Sequence in context: A070455 A070454 A070453 * A070653 A304233 A357556

Adjacent sequences: A070449 A070450 A070451 * A070453 A070454 A070455

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved