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%I #7 Feb 05 2015 10:16:31
%S 3,5,7,11,13,19,23,29,31,37,43,47,53,59,61,67,71,79,83,89,101,103,107,
%T 127,131,139,149,151,157,163,167,173,179,181,191
%N Numbers n for which all nontrivial cycles of the Ducci map have the same length.
%C All nontrivial cycles have the same length when either n is a prime number with primitive root 2 (see A001122) or when all factors of polynomial (x+1)^n+1 (mod 2) have the same multiplicative order. It is conjectured that all terms of this sequence are prime numbers. The cycle lengths for these n are in A138006.
%H 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 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 Cf. A038553, A138005 (primes not in this sequence).
%K nonn,more
%O 1,1
%A _T. D. Noe_, Feb 26 2008