The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

%I #4 Oct 07 2013 21:42:23

%S 1,13,15,1,29,285,34,35,1,53,14,21,51533,62,7,1,85,5,1299599,93,17765,

%T 16445,2,11,1,5,1155,1610,112897,1221,85183670,35,141,142,143,1,173,

%U 8645,4485,182,185,1677,1580795,101177,235613,8647745897021,194,195,1,229

%N 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, ...].

%e f(sqrt(2)) = f([1,2,2,...]) = [2,3,3,...] = (1 + sqrt(13)/2, so a(2) = 13.

%t \$MaxExtraPrecision = Infinity;

%t c[x_] := c[x] = FromContinuedFraction[ContinuedFraction[x] + 1]

%t Table[c[Sqrt[n]], {n, 1, 30}]

%t f[y_] := Cases[y, x_^(1/2 | -1/2) :> x, Infinity];

%t t = Table[f[c[Sqrt[n]]], {n, 1, 80}]; Flatten[t /. {} -> 1] (*A229957*)

%Y Cf. A229956, A229958, A229959.

%K nonn

%O 1,2

%A _Clark Kimberling_, Oct 04 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 6 18:55 EDT 2024. Contains 374981 sequences. (Running on oeis4.)