A038553 Maximum cycle length in differentiation digraph for n-bit binary sequences.

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

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