A070475 a(n) = n^3 mod 13.

0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1

Offset

0,3

Comments

Periodic with period length = 13. - Harvey P. Dale, Sep 24 2023

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, 0, 1).

Formula

From G. C. Greubel, Mar 28 2016: (Start)

a(n) = a(n-13).

G.f.: (-x - 8*x^2 - x^3 - 12*x^4 - 8*x^5 - 8*x^6 - 5*x^7 - 5*x^8 - x^9 - 12*x^10 - 5*x^11 - 12*x^12)/(-1 + x^13). (End)

Mathematica

Table[Mod[n^3, 13], {n, 0, 100}] (* G. C. Greubel, Mar 28 2016 *)
PowerMod[Range[0, 100], 3, 13] (* or *) PadRight[{}, 100, {0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12}] (* Harvey P. Dale, Sep 24 2023 *)

Prog

(Sage) [power_mod(n, 3, 13 )for n in range(0, 93)] # Zerinvary Lajos, Oct 29 2009
(PARI) a(n)=n^3%13 \\ Charles R Greathouse IV, Apr 06 2016

Crossrefs

Sequence in context: A099614 A032012 A092702 * A045771 A070488 A349142

Adjacent sequences: A070472 A070473 A070474 * A070476 A070477 A070478

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved