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

Author

N. J. A. Sloane, May 13 2002

Keywords

• nonn
• easy

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Programs

Magma

[Modexp(n, 4, 13): n in [0..100]]; // Vincenzo Librandi, Apr 02 2016 - after Bruno Berselli in A070403.

Mathematica

PowerMod[Range[0, 100], 4, 13] (* G. C. Greubel, Apr 01 2016 *)

PARI

a(n)=n^4%13 \\ Charles R Greathouse IV, Apr 06 2016

Sage

[power_mod(n,4,13)for n in range(0, 101)] # Zerinvary Lajos, Oct 31 2009

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)