A229958 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,...].

1, 5, 3, 1, 10, 42, 330, 11, 1, 17, 110, 2, 219962, 910, 42, 1, 26, 15, 6162806, 110, 371795, 933478, 510, 255, 1, 37, 462, 28985, 1329410, 39, 266477057, 4807, 4389, 3990, 10, 1, 2, 203, 462, 1295, 15130, 210, 3742742978, 9318265, 1898195, 66915741571718

Offset

1,2

Links

Table of n, a(n) for n=1..46.

Example

f(sqrt(2)) = f([1,2,2,...]) = [3,4,4,...] = 1 + sqrt(5), so a(2) = 5.

Mathematica

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] (*A229958*)
(* Peter J. C. Moses, Oct 04 2013 *)

Crossrefs

Cf. A229956, A229957, A229959.

Sequence in context: A011363 A021192 A074396 * A157891 A173644 A115991

Adjacent sequences: A229955 A229956 A229957 * A229959 A229960 A229961

Keyword

nonn

Author

Clark Kimberling, Oct 04 2013

Status

approved