A229958 - OEIS

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

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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*)