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

Author

Wolfdieter Lang, Jun 25 2018

Keywords

• nonn

Comments

See A305313 for comments, and A002559 for references.

Examples

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

Crossrefs

Cf. A002559, A305312, A305313.

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.