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A240072 Least number k with continued fraction of sqrt(k) having periodic part of length 2*n. 2
3, 7, 19, 31, 43, 46, 134, 94, 139, 151, 166, 271, 211, 334, 379, 463, 331, 478, 619, 526, 571, 604, 694, 631, 1051, 751, 886, 1039, 1141, 919, 1291, 1324, 1699, 1879, 1366, 2476, 2038, 1516, 1894, 1759, 2164, 1831, 2179, 1726, 2851, 2461, 2011, 2311, 4603 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It appears that, in general, these numbers are less than the corresponding numbers for the odd lengths, A062769.
LINKS
EXAMPLE
The continued fractions of sqrt(3), sqrt(7), and sqrt(19) are {1; 1, 2}, {2; 1, 1, 1, 4}, and {4; 2, 1, 3, 1, 2, 8}.
MATHEMATICA
nn = 50; t = Table[0, {nn}]; n = 1; found = 0; While[found < nn, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[EvenQ[len] && len/2 <= nn && t[[len/2]] == 0, t[[len/2]] = n; found++]]]; t
CROSSREFS
Cf. A013646 (even and odd), A062769 (similar, but odd length).
Sequence in context: A358238 A136054 A006032 * A066148 A093932 A141173
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 04 2014
STATUS
approved

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Last modified April 21 23:54 EDT 2024. Contains 371886 sequences. (Running on oeis4.)