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A271378 a(n) = 5^n mod 31. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A070387

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

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Last modified June 25 21:43 EDT 2019. Contains 324357 sequences. (Running on oeis4.)