A138004 Numbers n for which all nontrivial cycles of the Ducci map have the same length.

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

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