

A305314


Second member m_2(n) of the Markoff triple MT(n) with largest member m(n) = A002559(n), and smallest member m_1(n) = A305313(n), for n >= 1. These triples are conjectured to be unique.


3



1, 1, 2, 5, 5, 13, 34, 29, 13, 89, 29, 233, 169, 34, 610, 194, 1597, 985, 433, 194, 89, 4181, 169, 10946, 5741, 433, 2897, 1325, 233, 28657, 6466, 1325, 33461, 75025, 7561, 610, 985, 196418, 43261, 9077, 195025, 14701, 514229, 96557, 2897, 51641, 9077, 1597, 37666, 1346269, 7561, 1136689, 14701, 6466, 3524578, 646018, 294685, 135137, 62210, 5741
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OFFSET

1,3


COMMENTS

See A305313 for comments, and A002559 for references.


LINKS

Table of n, a(n) for n=1..60.


FORMULA

a(n) = m_2(n) is the fundamental proper solution y of the indefinite binary quadratic form x^2  3*m(n)*x*y + y^2, of discriminant D(n) = 9*m(n)^2  4 = A305312(n), representing m(n)^2, for n >= 1, with x <= y. The uniqueness conjecture means that there are no other such fundamental solutions.


EXAMPLE

See A305313 for the first Markoff triples MT(n).


CROSSREFS

Cf. A002559, A305312, A305313.
Sequence in context: A144293 A174098 A183419 * A154694 A154696 A154698
Adjacent sequences: A305311 A305312 A305313 * A305315 A305316 A305317


KEYWORD

nonn


AUTHOR

Wolfdieter Lang, Jun 25 2018


STATUS

approved



