1,3

Number of points of period n in the simplest nontrivial disconnected S-integer dynamical system.

This sequence comes from the simplest disconnected S-integer system that is not hyperbolic. In the terminology of the papers referred to, it is constructed by choosing the under- lying field to be F_2(t), the element to be t and the nontrivial valuation to correspond to the polynomial 1+t. Since it counts periodic points, it satisfies the nontrivial congruence sum_{d|n}mu(d)a(n/d) = 0 mod n for all n and since it comes from a group automorphism it is a divisibility sequence.

Vijay Chothi: Periodic Points in S-integer dynamical systems. PhD thesis, University of East Anglia, 1996.

Vijay Chothi, Graham Everest, Thomas Ward. S-integer dynamical systems: periodic points. J. Reine Angew Math. 489 (1997), 99-132.

T. Ward. Almost all S-integer dynamical systems have many periodic points. Ergodic Th. Dynam. Sys. 18 (1998), 471-486.

R. Brown and J. L. Merzel, The number of Ducci sequences with a given period, Fib. Quart., 45 (2007), 115-121.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Chothi's thesis

a(24) = 2^16 = 65536 because ord_2(24)=3, so 24-2^ord_2(24)=16.

readlib(ifactors): for n from 1 to 100 do if n mod 2 = 1 then ord2 := 0 else ord2 := ifactors(n)[2][1][2] fi: printf(`%d, `, 2^(n-2^ord2)) od:

Cf. A000079, A006519, A129760.

Sequence in context: A117438 A075499 A099394 this_sequence A002568 A111661 A072651

Adjacent sequences: A059988 A059989 A059990 this_sequence A059992 A059993 A059994

easy,nonn

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Mar 15 2001