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

Author

Vincenzo Librandi, Apr 06 2016

Keywords

• nonn
• easy

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).

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).

Programs

Magma

[Modexp(5, n, 31): n in [0..100]];

Magma

&cat [[1,5,25]^^30]; // Bruno Berselli, Apr 07 2016

Maple

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

Mathematica

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

PARI

x='x+O('x^99); Vec((1+5*x+25*x^2)/(1-x^3)) \\ Altug Alkan, Apr 06 2016

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

Extensions

Edited by Bruno Berselli, Apr 07 2016