A187532 a(n) = 4^n mod 19.

1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5, 1, 4, 16, 7, 9, 17, 11, 6, 5

Offset: 0

Author

M. F. Hasler, Mar 10 2011

Keywords

• nonn
• easy

Comments

Period 9: repeat (1,4,16,7,9,17,11,6,5).

Also continued fraction expansion of (13140908+sqrt(323139488118562))/24969762. - Bruno Berselli, Sep 09 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A036120, A070342, A070373, A070395, A070421.

Programs

Magma

[4^n mod 19 : n in [0..80]]; // Vincenzo Librandi, Sep 09 2011

Mathematica

PowerMod[4, Range[0, 100], 19]  (* or *)
PadRight[{}, 100, {1, 4, 16, 7, 9, 17, 11, 6, 5}] (* Paolo Xausa, Mar 17 2024 *)

PARI

a(n)=lift(Mod(4,19)^n) \\ Charles R Greathouse IV, Mar 22 2016

Formula

a(n+9) = a(n).

G.f.: (1 + 4*x + 16*x^2 + 7*x^3 + 9*x^4 + 17*x^5 + 11*x^6 + 6*x^7 + 5*x^8)/((1-x)*(1+x+x^2)*(1+x^3+x^6)). - Bruno Berselli, Sep 09 2011