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A229957
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a(n) is the number m such that f(sqrt(n)) is in the field Q(sqrt(m)), where f(x) is defined from the continued fraction x = [c(0), c(1), ... ] as [c(0) + 1, c(1) + 1, ...].
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4
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1, 13, 15, 1, 29, 285, 34, 35, 1, 53, 14, 21, 51533, 62, 7, 1, 85, 5, 1299599, 93, 17765, 16445, 2, 11, 1, 5, 1155, 1610, 112897, 1221, 85183670, 35, 141, 142, 143, 1, 173, 8645, 4485, 182, 185, 1677, 1580795, 101177, 235613, 8647745897021, 194, 195, 1, 229
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OFFSET
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1,2
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LINKS
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EXAMPLE
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f(sqrt(2)) = f([1,2,2,...]) = [2,3,3,...] = (1 + sqrt(13)/2, so a(2) = 13.
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MATHEMATICA
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$MaxExtraPrecision = Infinity;
c[x_] := c[x] = FromContinuedFraction[ContinuedFraction[x] + 1]
Table[c[Sqrt[n]], {n, 1, 30}]
f[y_] := Cases[y, x_^(1/2 | -1/2) :> x, Infinity];
t = Table[f[c[Sqrt[n]]], {n, 1, 80}]; Flatten[t /. {} -> 1] (*A229957*)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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