A309376 a(n) appears in the congruences modulo 4 or 32 of Markoff numbers m(n) = A002559(n) for odd or even m(n).

0, 0, 1, 3, 7, 1, 22, 42, 6, 58, 108, 19, 246, 331, 399, 724, 1045, 1435, 202, 1890, 2269, 342, 3675, 7164, 8365, 1177, 10815, 12910, 1944, 18756, 24139, 33784, 48756, 6138, 73671, 106597, 124848, 128557, 20188, 231441, 284172, 39963, 336567, 360472, 421512, 62896, 605881, 730627, 819127, 110143, 1100122, 1656277, 232918, 2099832, 2306866, 2411752, 358911, 3445662

Offset

1,4

Comments

See the Aigner reference, Proposition 3.13., p. 55.

If m(n) is odd then m(n) = 1 + 4*a(n), and if m(n) is even then m(n) = 2 + 32* a(n).

References

Martin Aigner, Markov's Theorem and 100 Years of the Uniqueness Conjecture, Springer, 2013, p. 55.

Links

Table of n, a(n) for n=1..58.

Formula

If m(n) is odd then a(n) = (m(n) - 1)/4, and if m(n) is even then a(n) = (m(n) - 2)/32, for the Markoff numbers m(n) = A002559(n), for n >= 1.

Example

a(3) = 1 because m(3) - 1 = 4 = a(3)*4. m(3) is odd.
a(6) = 1 because m(6) - 2 = 32 = a(6)*32. m(6) is even.

Crossrefs

Cf. A002559.

Sequence in context: A316665 A110238 A077505 * A247382 A031436 A144556

Adjacent sequences: A309373 A309374 A309375 * A309377 A309378 A309379

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 26 2019

Status

approved