This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038553 #45 Jul 28 2025 10:54:26
%S A038553 1,1,3,1,15,6,7,1,63,30,341,12,819,14,15,1,255,126,9709,60,63,682,
%T A038553 2047,24,25575,1638,13797,28,475107,30,31,1,1023,510,4095,252,3233097,
%U A038553 19418,4095,120,41943,126,5461,1364,4095,4094,8388607,48,2097151,51150,255,3276,3556769739,27594,1048575
%N A038553 Maximum cycle length in differentiation digraph for n-bit binary sequences.
%C A038553 Length of longest cycle for vectors of length n under the Ducci map.
%C A038553 Also, the period of polynomial (x+1)^n+1 over GF(2) (cf. A046932). - _Max Alekseyev_, Oct 12 2013
%C A038553 Per the comment by _T. D. Noe_ originally given in A138006, it appears that for an odd n > 1, a(n) <= n*(2^((n-1)/2)-1). - _Max Alekseyev_, Jul 10 2025
%D A038553 Simmons, G. J., The structure of the differentiation digraphs of binary sequences. Ars Combin. 35 (1993), A, 71-88. Math. Rev. 95f:05052.
%H A038553 Max Alekseyev, <a href="/A038553/b038553.txt">Table of n, a(n) for n = 1..2458</a>
%H A038553 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 A038553 N. J. Calkin, J. G. Stevens, D. M. Thomas, <a href="https://web.archive.org/web/20240208212446/https://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 A038553 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).]
%F A038553 It appears that whenever b(n) = log2(a(n)/n + 1) is an integer and n > 1, b(n) = A119513(n) = A136043(n). - _Andrei Zabolotskii_, Jul 28 2025
%Y A038553 Cf. A111944, A135547, A136043, A119513.
%K A038553 nonn
%O A038553 1,3
%A A038553 _N. J. A. Sloane_
%E A038553 Entry revised by _N. J. A. Sloane_, Jun 19 2006, Feb 24 2008
%E A038553 a(46) corrected, terms a(51) onward and b-file added by _Max Alekseyev_, Oct 12 2013
%E A038553 b-file extended by _Max Alekseyev_, Sep 24 2019