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 A229959 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)^2, c(1)^2, ...]. 3
 1, 5, 2, 1, 65, 17, 3, 5, 1, 13, 82, 37, 346, 798, 10, 1, 41, 257, 72829155, 65, 4238, 269, 3, 17, 1, 2501, 626, 2039422, 2522, 101, 3303936030, 2567, 646, 23358, 26, 1, 5185, 1297, 577, 13, 1507985, 145, 15004500051, 189987, 445445, 143733855087930, 431211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..47. EXAMPLE f(sqrt(2)) = f([1,2,2,...]) = [1,4,4,...] = -1 + sqrt(5), so a(2) = 5. MATHEMATICA \$MaxExtraPrecision = Infinity; c[x_] := c[x] = FromContinuedFraction[ContinuedFraction[x]^2] 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] (* Peter J. C. Moses, Oct 04 2013 *) CROSSREFS Cf. A229956, A229957, A229958. Sequence in context: A109281 A133289 A107719 * A174485 A334343 A285641 Adjacent sequences: A229956 A229957 A229958 * A229960 A229961 A229962 KEYWORD nonn AUTHOR Clark Kimberling, Oct 04 2013 STATUS approved

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Last modified August 3 08:07 EDT 2024. Contains 374885 sequences. (Running on oeis4.)