

A038553


Maximum cycle length in differentiation digraph for nbit binary sequences.


5



1, 1, 3, 1, 15, 6, 7, 1, 63, 30, 341, 12, 819, 14, 15, 1, 255, 126, 9709, 60, 63, 682, 2047, 24, 25575, 1638, 13797, 28, 475107, 30, 31, 1, 1023, 510, 4095, 252, 3233097, 19418, 4095, 120, 41943, 126, 5461, 1364, 4095, 4094, 8388607, 48, 2097151, 51150, 255, 3276, 3556769739, 27594, 1048575
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OFFSET

1,3


COMMENTS

Length of longest cycle for vectors of length n under the Ducci map.
Also, the period of polynomial (x+1)^n+1 over GF(2) (cf. A046932).  Max Alekseyev, Oct 12 2013


REFERENCES

Simmons, G. J., The structure of the differentiation digraphs of binary sequences. Ars Combin. 35 (1993), A, 7188. Math. Rev. 95f:05052.


LINKS

Max Alekseyev, Table of n, a(n) for n = 1..2458
Florian Breuer, Igor E. Shparlinski, Lower bounds for periods of Ducci sequences, arXiv:1909.04462 [math.NT], 2019.
N. J. Calkin, J. G. Stevens, D. M. Thomas, A characterization for the lengths of cycles of the nnumber Ducci game, Fib. Q., 43 (No. 1, 2005), 5359.
O. N. Karpenkov, On examples of difference operators for {0,1}valued functions over finite sets, Funct. Anal. Other Math. 1 (2006), 175180. [Gives incorrect value 4095 for a(46).]


CROSSREFS

Cf. A111944, A135547
Sequence in context: A089463 A136231 A113389 * A282629 A135896 A134144
Adjacent sequences: A038550 A038551 A038552 * A038554 A038555 A038556


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Entry revised by N. J. A. Sloane, Jun 19 2006, Feb 24 2008
a(46) corrected, terms a(51) onward and bfile added by Max Alekseyev, Oct 12 2013
bfile extended by Max Alekseyev, Sep 24 2019


STATUS

approved



