A324601 -id:A324601 - cp's OEIS frontend

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

Wolfdieter Lang, Jul 26 2019

nonn

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).

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

Cf. A002559, A324601.

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

cp's OEIS Frontend

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.

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