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A038553 Maximum cycle length in differentiation digraph for n-bit 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 (list; graph; refs; listen; history; text; internal format)
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, 71-88. 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 n-number Ducci game, Fib. Q., 43 (No. 1, 2005), 53-59.

O. N. Karpenkov, On examples of difference operators for {0,1}-valued functions over finite sets, Funct. Anal. Other Math. 1 (2006), 175-180. [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 b-file added by Max Alekseyev, Oct 12 2013

b-file extended by Max Alekseyev, Sep 24 2019

STATUS

approved

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Last modified August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)