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A082991
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Define a sequence u as follows: u(1)=n, thereafter u(2k)=sigma(u(2k-1)), u(2k+1)=phi(u(2k)); then a(n) is the length of the period of u(k) (which is conjectured to becoming ultimately periodic for any n>=1).
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1, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 2, 4, 2, 2, 6, 4, 6, 2, 2, 6, 2, 2, 6, 6, 2, 6, 6, 2, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 2, 4, 2, 6, 6, 6, 6, 4, 4, 4, 6, 4, 6, 4, 6, 4, 4, 6, 6, 4, 6, 4, 4, 4, 6, 4, 4, 4, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 6, 4, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Conjecture: despite results for small terms, all even number are reached. (ex. 12 is reached since a(12102)=12).
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REFERENCES
| J. Berstel et al., Combinatorics on Words: Christoffel Words and Repetitions in Words, Amer. Math. Soc., 2008. See p. 83.
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EXAMPLE
| If n=6, u(1)=6, u(2)=sigma(6)=12, u(3)=phi(12)=4, u(4)=sigma(4)=7 u(5)=phi(7)=6, hence u(k) becomes periodic with period (6,12,4,7) of length 4 and a(6)=4.
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CROSSREFS
| Sequence in context: A182730 A152858 A091248 * A100008 A102763 A054844
Adjacent sequences: A082988 A082989 A082990 * A082992 A082993 A082994
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), May 29 2003
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