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 A309376 a(n) appears in the congruences modulo 4 or 32 of Markoff numbers m(n) = A002559(n) for odd or even m(n). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 23 17:42 EDT 2023. Contains 365554 sequences. (Running on oeis4.)