A309161 a(n) = (x(n)^2 + 1)/m(n), with m(n) = A002559(n) (Markoff numbers) and x(n)= A324601(n), for n >= 3. The Markoff uniqueness conjecture is assumed to be true.

1, 2, 5, 5, 13, 29, 29, 34, 74, 29, 34, 25, 233, 433, 202, 985, 457, 1130, 541, 1597, 2042, 4181, 5741, 145, 6466, 7561, 2957, 2378, 16501, 5, 3733, 1157, 53, 62210, 27845, 75025, 96557, 43970, 59153, 5857, 160373, 219658, 252005, 294685, 126226, 426389, 559945, 514229, 733, 514, 1278649, 706225, 3001, 1441889, 1716469, 61913, 187045, 12994

Offset

3,2

Comments

See the Aigner reference, Corollary 3.17., p. 58.

If the equation x^2 + 1 = a(n)*m(n), with m(n) = A002559(n) holds for just one integral x = x(n) in the interval [1, floor(m(n)/2)] then the Markoff uniqueness conjecture is true. x(n) = A324601(n) (if the Markoff conjecture holds).

References

Martin Aigner, Markov's Theorem and 100 Years of the Uniqueness Conjecture, Springer, 2013, p. 58.

Links

Table of n, a(n) for n=3..60.

Formula

a(n) = (A324601(n)^2 + 1)/A002559(n), for n >= 3.

Crossrefs

Cf. A002559, A324601.

Sequence in context: A326637 A303355 A154692 * A144293 A174098 A183419

Adjacent sequences: A309158 A309159 A309160 * A309162 A309163 A309164

Keyword

nonn

Author

Wolfdieter Lang, Jul 26 2019

Status

approved