A266973 a(n) = 4^n mod 17.

1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16, 13, 1, 4, 16

Offset

0,2

Comments

Period 4: repeat [1, 4, 16, 13].

Links

Table of n, a(n) for n=0..74.

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

Formula

G.f.: (1+4*x+16*x^2+13*x^3)/(1-x^4).

a(n) = a(n-4) for n>3.

From Wesley Ivan Hurt, Jun 29 2016: (Start)

a(n) = (34 - 3*(5 + 3*I)*I^(-n) - 3*(5 - 3*I)*I^n)/4 where I=sqrt(-1).

a(n) = (17 - 15*cos(n*Pi/2) - 9*sin(n*Pi/2))/2. (End)

Maple

A266973:=n->power(4, n) mod 17: seq(A266973(n), n=0..100); # Wesley Ivan Hurt, Jun 29 2016

Mathematica

PowerMod[4, Range[0, 100], 17]

Prog

(Magma) [Modexp(4, n, 17): n in [0..100]];

Crossrefs

Cf. similar sequences of the type 4^n mod p, where p is a prime: A010685 (5), A153727 (7), A168429 (11), A168430 (13), this sequence (17), A187532 (19).

Sequence in context: A224123 A273579 A147560 * A029659 A265218 A331055

Adjacent sequences: A266970 A266971 A266972 * A266974 A266975 A266976

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 06 2016

Status

approved