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A309376
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a(n) appears in the congruences modulo 4 or 32 of Markoff numbers m(n) = A002559(n) for odd or even m(n).
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1
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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
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OFFSET
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1,4
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COMMENTS
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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).
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REFERENCES
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Martin Aigner, Markov's Theorem and 100 Years of the Uniqueness Conjecture, Springer, 2013, p. 55.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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