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Search: id:A082991
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| A082991 |
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Define sequence u as follows : u(1)=n, u(2k)=sigma(u(2k-1)), u(2k+1)=phi(u(2k)) then a(n) is the period length 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; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture : despite results for small terms, all even number are reached. (ex. 12 is reached since a(12102)=12).
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EXAMPLE
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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
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Sequence in context: A085191 A061142 A091248 this_sequence A100008 A054844 A057936
Adjacent sequences: A082988 A082989 A082990 this_sequence A082992 A082993 A082994
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 29 2003
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