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A277749
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Numerators of rationals R_n associated with an analog of Stern's diatomic sequence for Z[sqrt(2)].
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4
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2, 1, 4, 3, 2, 3, 4, 1, 6, 5, 4, 7, 10, 3, 8, 5, 2, 5, 8, 3, 10, 7, 4, 5, 6, 1, 8, 7, 6, 11, 16, 5, 14, 9, 4, 11, 18, 7, 24, 17, 10, 13, 16, 3, 14, 11, 8, 13, 18, 5, 12, 7, 2, 7, 12, 5, 18, 13, 8, 11, 14, 3, 16, 13, 10, 17, 24, 7, 18, 11, 4, 9, 14, 5, 16, 11, 6, 7, 8, 1, 10, 9, 8, 15, 22, 7, 20, 13
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OFFSET
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1,1
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COMMENTS
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"At the end of Section 6, the sequences of numerators and denominators of R_n were considered. What do these sequences count? Further, is there some kind of combinatorial reciprocity [Beck] occurring here?" - [S. Northshield]
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LINKS
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FORMULA
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EXAMPLE
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2, 1, 4, 3/2, 2/3, 3, 4/3, 1/2, 6, 5/3, 4/5, 7/2, 10/7, 3/5, 8/3, 5/4, 2/5, 5, 8/5, 3/4, ...
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MATHEMATICA
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R[1] = 2; R[n_] := R[n] = 4 IntegerExponent[n, 3] + 2 - 2/R[n-1];
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PROG
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(PARI)
seq(N) = {
my(v = vector(N)); v[1] = 2;
for (n = 2, N, v[n] = 4*valuation(n, 3) + 2 - 2 / v[n-1]);
return(v);
};
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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