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| A305317
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a(n) gives the length of the period of the regular continued fraction of the quadratic irrational of any Markoff form representative Mf(n), n >= 1 (assuming the uniqueness conjecture).
(history;
published version)
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#13 by Kevin Ryde at Sun May 29 19:58:51 EDT 2022
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#12 by Omar E. Pol at Sun May 29 19:37:55 EDT 2022
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#11 by Eric Rowland at Sun May 29 18:31:32 EDT 2022
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#10 by Eric Rowland at Sun May 29 18:31:13 EDT 2022
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| COMMENTS
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The index n enumerates the Markoff triples with largest member m from A002559 in increasing order. If the Markoff-Frobenius uniqueness conjecture (see, e.g. the book of Aigner) is true then the triples can be numbered by n if the largest member is m(n) = A00255A002559(n). In the other (unlikely) case there may be more than one triple (hence forms) for some Markoff numbers m from A002559, and then one orders these triples lexicographically.
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| STATUS
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approved
editing
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Discussion
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| Sun May 29
| 18:31
| Eric Rowland: Corrected sequence number
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#9 by N. J. A. Sloane at Sat Jan 19 04:15:43 EST 2019
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| COMMENTS
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The index n enumerates the Markoff triples with largest member m from A002559 in increasing order. If the Markoff-Frobenius uniqueness conjecture (see, e.g. the book of Aigner) is true then the triples can be numbered by n if the largest member is m(n) = A00255(n). In the other (unlikely) case there may be more than one triplettriple (hence forms) for some Markoff numbers m from A002559, and then one orders these triples lexicographically.
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Discussion
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| Sat Jan 19
| 04:15
| OEIS Server: https://oeis.org/edit/global/2799
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#8 by N. J. A. Sloane at Sat Jan 19 04:14:59 EST 2019
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| COMMENTS
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The index n enumerates the Markoff triples with largest member m from A002559 in increasing order. If the Markoff-Frobenius uniqueness conjecture (see, e.g. the book of Aigner) is true then the tripletstriples can be numbered by n if the largest member is m(n) = A00255(n). In the other (unlikely) case there may be more than one triplet (hence forms) for some Markoff numbers m from A002559, and then one orders these tripletstriples lexicographically.
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Discussion
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| Sat Jan 19
| 04:14
| OEIS Server: https://oeis.org/edit/global/2798
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#7 by N. J. A. Sloane at Tue Jul 31 10:04:34 EDT 2018
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#6 by N. J. A. Sloane at Tue Jul 31 10:04:13 EDT 2018
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| COMMENTS
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The index n numeratesenumerates the Markoff triples with largest member m from A002559 in increasing order. If the Markoff-Frobenius uniqueness conjecture (see, e.g. the book of Aigner) is true then the triplets can be numbered by n if the largest member is m(n) = A00255(n). In the other (unlikely) case there may be more than one triplet (hence forms) for some Markoff numbers m from A002559, and then one orders these triplets lexicographically.
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proposed
editing
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Discussion
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| Tue Jul 31
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| N. J. A. Sloane: a minor edit
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#5 by Michel Marcus at Mon Jul 30 09:27:43 EDT 2018
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#4 by Michel Marcus at Mon Jul 30 09:27:39 EDT 2018
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| EXAMPLE
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The periods for the representative form Mf(n) with k(n) = A305311(n) are given for n=1..40 in the W. Lang link in Table 2.
given for n=1..40 in the W. Lang link in Table 2. The first 11 examples (given by Perron) are:
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proposed
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