A070517 a(n) = n^4 mod 13.

0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9

Offset

0,3

Comments

Equivalently: n^(12*m + 4) mod 13. - G. C. Greubel, Apr 01 2016

Links

Table of n, a(n) for n=0..100.

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, Apr 01 2016: (Start)

a(n+13) = a(n).

a(13*m) = 0.

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

Mathematica

PowerMod[Range[0, 100], 4, 13] (* G. C. Greubel, Apr 01 2016 *)
PadRight[{}, 120, {0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1}] (* Harvey P. Dale, Jan 30 2026 *)

Prog

(SageMath) [power_mod(n, 4, 13)for n in range(0, 101)] # Zerinvary Lajos, Oct 31 2009
(Magma) [Modexp(n, 4, 13): n in [0..100]]; // Vincenzo Librandi, Apr 02 2016 - after Bruno Berselli in A070403.
(PARI) a(n)=n^4%13 \\ Charles R Greathouse IV, Apr 06 2016

Crossrefs

Sequence in context: A140059 A392595 A324895 * A290408 A028232 A225359

Adjacent sequences: A070514 A070515 A070516 * A070518 A070519 A070520

Keyword

nonn,easy

Author

N. J. A. Sloane, May 13 2002

Status

approved