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A070365
a(n) = 5^n mod 7.
6
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)
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).
Sequence in context: A176317 A092426 A255291 * A368666 A190613 A161011
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 12 2002
STATUS
approved