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A138004
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Numbers n for which all nontrivial cycles of the Ducci map have the same length.
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2
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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; internal format)
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OFFSET
| 1,1
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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.
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REFERENCES
| 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.
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CROSSREFS
| Cf. A038553, A138005 (primes not in this sequence).
Sequence in context: A109358 A192862 A110589 * A045395 A191377 A095070
Adjacent sequences: A138001 A138002 A138003 * A138005 A138006 A138007
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Feb 26 2008
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