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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

%I #10 Aug 01 2019 05:41:36

%S 0,0,1,3,7,1,22,42,6,58,108,19,246,331,399,724,1045,1435,202,1890,

%T 2269,342,3675,7164,8365,1177,10815,12910,1944,18756,24139,33784,

%U 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

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

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

%C 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).

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

%F 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.

%e a(3) = 1 because m(3) - 1 = 4 = a(3)*4. m(3) is odd.

%e a(6) = 1 because m(6) - 2 = 32 = a(6)*32. m(6) is even.

%Y Cf. A002559.

%K nonn,easy

%O 1,4

%A _Wolfdieter Lang_, Jul 26 2019

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Last modified December 7 18:28 EST 2023. Contains 367660 sequences. (Running on oeis4.)