A229956 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 [1/c(0), 1/c(1), ...].

1, 17, 1, 1, 65, 33, 33, 17, 1, 145, 73, 1, 73, 1105, 1, 1, 257, 129, 24465, 65, 129, 97, 2737, 33, 1, 401, 201, 57889, 353, 1, 32929, 161, 105, 609, 41, 1, 577, 1, 193, 145, 481, 97, 142809601, 28985, 2497, 337, 385, 1, 1, 785, 393, 36985, 254473, 219185

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Example

f(sqrt(2)) = f([1,2,2,...]) = [1,1/2,1/2,...] = (3 + sqrt(17))/4, so a(2) = 17.

Mathematica

$MaxExtraPrecision = Infinity;
c[x_] := c[x] = FromContinuedFraction[1/ContinuedFraction[x]]
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. A229957, A229958, A229959.

Sequence in context: A190580 A176203 A103637 * A157274 A218115 A144442

Adjacent sequences: A229953 A229954 A229955 * A229957 A229958 A229959

Keyword

nonn

Author

Clark Kimberling, Oct 04 2013

Status

approved