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, ...].

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

Offset

1,2

Links

Table of n, a(n) for n=1..50.

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

Cf. A229956, A229958, A229959.

Sequence in context: A041835 A042505 A156371 * A070640 A043657 A043702

Adjacent sequences: A229954 A229955 A229956 * A229958 A229959 A229960

Keyword

nonn

Author

Clark Kimberling, Oct 04 2013

Status

approved