

A059990


Number of points of period n under the dual of the map x>2x on Z[1/6].


2



1, 1, 7, 5, 31, 7, 127, 85, 511, 341, 2047, 455, 8191, 5461, 32767, 21845, 131071, 9709, 524287, 349525, 2097151, 1398101, 8388607, 1864135, 33554431, 22369621, 134217727, 89478485, 536870911, 119304647
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OFFSET

1,3


COMMENTS

This sequence counts the periodic points in the simplest nontrivial Sinteger dynamical system. These dynamical systems arise naturally in arithmetic and are built by making an isometric extension of a familiar hyperbolic system. The extension destroys some of the periodic points, in this case reducing the original number 2^n1 by factoring out any 3's. An interesting feature is that the logarithmic growth rate is still log 2.
A059990[n+7] times some power of 3 seems to me the greatest common Denominator of A035522[4n+16+1],A035522[4n+16+2],A035522[4n+16+3] and A035522[4n+16+4] for n>1 [From Dylan Hamilton, Aug 04 2010]


REFERENCES

V. Chothi, G. Everest, T. Ward. Sinteger dynamical systems: periodic points. J. Reine Angew. Math., 489 (1997), 99132.
T. Ward. Almost all Sinteger dynamical systems have many periodic points. Erg. Th. Dynam. Sys. 18 (1998), 471486.


LINKS

Table of n, a(n) for n=1..30.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.


FORMULA

a(n)=(2^n1)x2^n1_3


EXAMPLE

a(6)=7 because 2^61 = 3^2x7, so 2^61_3=3^(2).


CROSSREFS

Cf. A000225, A001945, A059991.
Sequence in context: A226661 A120404 A146619 * A213246 A213243 A185269
Adjacent sequences: A059987 A059988 A059989 * A059991 A059992 A059993


KEYWORD

easy,nonn


AUTHOR

Thomas Ward (t.ward(AT)uea.ac.uk), Mar 08 2001


STATUS

approved



