A070365 a(n) = 5^n mod 7.

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

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

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 * A368666 A190613 A161011

Adjacent sequences: A070362 A070363 A070364 * A070366 A070367 A070368

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved