cp's OEIS Frontend

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.

A138004 Odd numbers k for which all nontrivial cycles of the Ducci map on k-tuples modulo 2 have the same length.

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%I A138004 #17 Jul 11 2025 14:17:16
%S A138004 3,5,7,11,13,19,23,29,31,37,43,47,53,59,61,67,71,79,83,89,101,103,107,
%T A138004 127,131,139,149,151,157,163,167,173,179,181,191,197,199,211,223,227,
%U A138004 233,239,251,263,269,271,281,283,293,307,311,313,317,347,349,359,367,373,379,383,389
%N A138004 Odd numbers k for which all nontrivial cycles of the Ducci map on k-tuples modulo 2 have the same length.
%C A138004 All nontrivial cycles have the same length when either k is a prime number with primitive root 2 (see A001122), or when all factors of polynomial ((x+1)^k+1)/x (mod 2) have the same multiplicative order. The corresponding cycle lengths are listed in A138006.
%C A138004 It is conjectured that all terms of this sequence are prime numbers.
%C A138004 Numbers k such that A111944(k) = 2. - _Max Alekseyev_, Jul 10 2025
%H A138004 Max Alekseyev, <a href="/A138004/b138004.txt">Table of n, a(n) for n = 1..310</a>
%H A138004 Florian Breuer, Ernest Lotter and Brink van der Merve, <a href="http://dx.doi.org/10.1016/j.ffa.2005.11.003">Ducci sequences and cyclotomic polynomials</a>, Finite Fields Appl. 13 (2007), 293-304.
%H A138004 Michal Misiurewicz, John G. Stevens and Diana M. Thomas, <a href="http://dx.doi.org/10.1016/j.laa.2005.09.002">Iterations of Linear Maps over Finite Fields</a>, Linear Algebra and its Applications, Vol. 413 (2006), 218-234.
%Y A138004 Cf. A001122, A038553, A111944, A138005, A138006.
%K A138004 nonn
%O A138004 1,1
%A A138004 _T. D. Noe_, Feb 26 2008
%E A138004 Edited and terms a(36) onward added by _Max Alekseyev_, Jul 10 2025