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A138004 Numbers n for which all nontrivial cycles of the Ducci map have the same length. 2
3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 83, 89, 101, 103, 107, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..35.

Florian Breuer, Ernest Lotter and Brink van der Merve, Ducci sequences and cyclotomic polynomials, Finite Fields Appl. 13 (2007), 293-304.

Michal Misiurewicz, John G. Stevens and Diana M. Thomas, Iterations of Linear Maps over Finite Fields, Linear Algebra and its Applications, Vol. 413 (2006), 218-234.

CROSSREFS

Cf. A038553, A138005 (primes not in this sequence).

Sequence in context: A216285 A192862 A110589 * A045395 A191377 A095070

Adjacent sequences:  A138001 A138002 A138003 * A138005 A138006 A138007

KEYWORD

nonn,more

AUTHOR

T. D. Noe, Feb 26 2008

STATUS

approved

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Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)