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A180853
Trajectory of 4 under map n->A006368(n).
20
4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5
OFFSET
0,1
COMMENTS
The trajectory of 8 is a famous unsolved problem - see A028393.
REFERENCES
D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998; see p. 16.
FORMULA
Periodic with period of length 5.
G.f.: ( -4-6*x-9*x^2-7*x^3-5*x^4 ) / ( (x-1)*(1+x+x^2+x^3+x^4) ). - R. J. Mathar, Mar 10 2011
a(n+1) = A006368(a(n)).
a(n) = a(n-5). - Wesley Ivan Hurt, Apr 26 2021
MATHEMATICA
Table[{4, 6, 9, 7, 5}, {21}] // Flatten (* Jean-François Alcover, Jun 10 2013 *)
PadRight[{}, 120, {4, 6, 9, 7, 5}] (* Harvey P. Dale, Jul 11 2020 *)
PROG
(Haskell)
a180853 n = a180853_list !! n
a180853_list = iterate a006368 4 -- Reinhard Zumkeller, Apr 18 2012
(PARI) Vec((-4-6*x-9*x^2-7*x^3-5*x^4)/((x-1)*(1+x+x^2+x^3+x^4))+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 22 2011
STATUS
approved