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A070365 a(n) = 5^n mod 7. 5
1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1, 5, 4, 6, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From Klaus Brockhaus, May 23 2010: (Start)

Period 6: repeat [1, 5, 4, 6, 2, 3].

Continued fraction expansion of (221+11*sqrt(1086))/490.

Decimal expansion of 199/1287.

First bisection is A153727. (End)

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = (1/30)*(17*(n mod 6)+2*((n+1) mod 6)+27*((n+2) mod 6)-3*((n+3) mod 6)+12*((n+4) mod 6)-13*((n+5) mod 6)). - Paolo P. Lava, Feb 24 2010

From R. J. Mathar, Apr 13 2010: (Start)

a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.

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

From Klaus Brockhaus, May 23 2010: (Start)

a(n+1)-a(n) = A178141(n).

a(n+2)-a(n) = A117373(n+5). (End)

From G. C. Greubel, Mar 05 2016: (Start)

a(n) = a(n-6) for n>5.

E.g.f.: (1/3)*(7*cosh(x) + 14*sinh(x) + 2*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) - 4*exp(x/2)*cos(sqrt(3)*x/2)). (End)

a(n) = (21 - 7*cos(n*Pi) - 8*cos(n*Pi/3) + 4*sqrt(3)*sin(n*Pi/3))/6. - Wesley Ivan Hurt, Jun 23 2016

a(n) = A010876(A000351(n)). - Michel Marcus, Jun 27 2016

MAPLE

A070365:=n->[1, 5, 4, 6, 2, 3][(n mod 6)+1]: seq(A070365(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

MATHEMATICA

PowerMod[5, Range[0, 110], 7] (* or *) LinearRecurrence[{1, 0, -1, 1}, {1, 5, 4, 6}, 110] (* Harvey P. Dale, Apr 26 2011 *)

Table[Mod[5^n, 7], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)

PadRight[{}, 100, {1, 5, 4, 6, 2, 3}] (* or *) CoefficientList[Series[(1 + 5 x + 4 x^2 + 6 x^3 + 2 x^4 + 3 x^5) / (1 - x^6), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 24 2016 *)

PROG

(PARI) a(n)=lift(Mod(5, 7)^n) \\ Charles R Greathouse IV, Mar 22 2016

(MAGMA) [Modexp(5, n, 7): n in [0..100]]; // Vincenzo Librandi, Mar 24 2016 - after Bruno Berselli

CROSSREFS

Cf. A178229 (decimal expansion of (221+11*sqrt(1086))/490), A178141 (repeat 4, -1, 2, -4, 1, -2), A117373 (repeat 1, -2, -3, -1, 2, 3), A153727 (trajectory of 3x+1 sequence starting at 1).

Cf. A000351, A010876.

Sequence in context: A176317 A092426 A255291 * A190613 A161011 A232734

Adjacent sequences:  A070362 A070363 A070364 * A070366 A070367 A070368

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 12 2002

STATUS

approved

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Last modified December 8 01:46 EST 2019. Contains 329850 sequences. (Running on oeis4.)