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A013645 Values of n at which period of continued fraction for sqrt(n) increases. 4
1, 2, 3, 7, 13, 19, 31, 43, 46, 94, 139, 151, 166, 211, 331, 421, 526, 571, 604, 631, 751, 886, 919, 1291, 1324, 1366, 1516, 1621, 1726, 2011, 2311, 2566, 2671, 3004, 3019, 3334, 3691, 3931, 4174, 4846, 5119, 6211, 6451, 6679, 6694, 7606, 8254, 8779, 8941, 9739 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Periods of the fractions (sequence offset by one term) are given by A020640.

For n = 1 to 513 (the range of the b-file), the class number of the field Q(sqrt(a(n))) is 1 (computed with Mathematica). - Emmanuel Vantieghem, Mar 16 2017-

REFERENCES

Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).

LINKS

T. D. Noe and Patrick McKinley, Table of n, a(n) for n = 1..513 (first 200 terms from T. D. Noe)

EXAMPLE

The continued fraction for Sqrt(31) is 5, {1, 1, 3, 5, 3, 1, 1, 10} and the continued fraction for Sqrt(43) is 6, {1, 1, 3, 1, 5, 1, 3, 1, 1, 12}; and there is no number between 31 and 43 whose square root produces a continued fraction the period of which exceeds the one for 31.

MATHEMATICA

mx = -1; t = {}; Do[len = Length[ Last[ ContinuedFraction[ Sqrt[ n]]]]; If[len > mx, mx = len; AppendTo[t, n]], {n, 10^4}]; t

CROSSREFS

Cf. A003285, A020640.

Sequence in context: A210393 A045331 A053613 * A130272 A172238 A319496

Adjacent sequences:  A013642 A013643 A013644 * A013646 A013647 A013648

KEYWORD

nonn,nice

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)