The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038553 Maximum cycle length in differentiation digraph for n-bit binary sequences. 5


%S 1,1,3,1,15,6,7,1,63,30,341,12,819,14,15,1,255,126,9709,60,63,682,

%T 2047,24,25575,1638,13797,28,475107,30,31,1,1023,510,4095,252,3233097,

%U 19418,4095,120,41943,126,5461,1364,4095,4094,8388607,48,2097151,51150,255,3276,3556769739,27594,1048575

%N Maximum cycle length in differentiation digraph for n-bit binary sequences.

%C Length of longest cycle for vectors of length n under the Ducci map.

%C Also, the period of polynomial (x+1)^n+1 over GF(2) (cf. A046932). - _Max Alekseyev_, Oct 12 2013

%D Simmons, G. J., The structure of the differentiation digraphs of binary sequences. Ars Combin. 35 (1993), A, 71-88. Math. Rev. 95f:05052.

%H Max Alekseyev, <a href="/A038553/b038553.txt">Table of n, a(n) for n = 1..2458</a>

%H Florian Breuer, Igor E. Shparlinski, <a href="https://arxiv.org/abs/1909.04462">Lower bounds for periods of Ducci sequences</a>, arXiv:1909.04462 [math.NT], 2019.

%H N. J. Calkin, J. G. Stevens, D. M. Thomas, <a href="http://www.fq.math.ca/Papers1/43-1/paper43-1-7.pdf">A characterization for the lengths of cycles of the n-number Ducci game</a>, Fib. Q., 43 (No. 1, 2005), 53-59.

%H O. N. Karpenkov, <a href="http://arxiv.org/abs/math/0611940">On examples of difference operators for {0,1}-valued functions over finite sets</a>, Funct. Anal. Other Math. 1 (2006), 175-180. [Gives incorrect value 4095 for a(46).]

%Y Cf. A111944, A135547

%K nonn

%O 1,3

%A _N. J. A. Sloane_.

%E Entry revised by _N. J. A. Sloane_, Jun 19 2006, Feb 24 2008

%E a(46) corrected, terms a(51) onward and b-file added by _Max Alekseyev_, Oct 12 2013

%E b-file extended by _Max Alekseyev_, Sep 24 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)