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URL: https://oeis.org/A309161

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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
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.
FORMULA
a(n) = (A324601(n)^2 + 1)/A002559(n), for n >= 3.
CROSSREFS
Sequence in context: A326637 A303355 A154692 * A144293 A174098 A183419
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Jul 26 2019
STATUS
approved