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.

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

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