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A229957 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, ...]. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
EXAMPLE
f(sqrt(2)) = f([1,2,2,...]) = [2,3,3,...] = (1 + sqrt(13)/2, so a(2) = 13.
MATHEMATICA
$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*)
CROSSREFS
Sequence in context: A041835 A042505 A156371 * A070640 A043657 A043702
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 04 2013
STATUS
approved

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Last modified July 23 04:10 EDT 2024. Contains 374544 sequences. (Running on oeis4.)