A271378 a(n) = 5^n mod 31.

1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25, 1, 5, 25

Offset

0,2

Comments

Period 3: repeat [1, 5, 25].

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1+5*x+25*x^2)/(1-x^3).

a(n) = a(n-3) for n>2.

a(n) = 5^(n mod 3).

a(n) = (31 - 28*cos(2*n*Pi/3) - 20*sqrt(3)*sin(2*n*Pi/3))/3. - Wesley Ivan Hurt, Jun 30 2016

Maple

seq(op([1, 5, 25]), n=0..50); # Wesley Ivan Hurt, Jun 30 2016

Mathematica

PowerMod[5, Range[0, 100], 31]

Prog

(Magma) [Modexp(5, n, 31): n in [0..100]];
(Magma) &cat [[1, 5, 25]^^30]; // Bruno Berselli, Apr 07 2016
(PARI) x='x+O('x^99); Vec((1+5*x+25*x^2)/(1-x^3)) \\ Altug Alkan, Apr 06 2016

Crossrefs

Cf. similar sequences of the type 5^n mod p, where p is a prime: A070365 (p=7), A070367 (p=11), A070368 (p=13), A070371 (p=17), A070373 (p=19), A036121 (p=23), A070379 (p=29), this sequence (p=31), A070384 (p=37), A070387 (p=41), A070389 (p=43), A036127 (p=47), A036133 (p=73), A036137 (p=97), A271379 (p=101), A036139 (p=103), A036149 (p=157), A271380 (p=163) A036151 (p=167), A036156 (p=193).

Sequence in context: A156310 A142725 A270590 * A305837 A175555 A346994

Adjacent sequences: A271375 A271376 A271377 * A271379 A271380 A271381

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 06 2016

Extensions

Edited by Bruno Berselli, Apr 07 2016

Status

approved