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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 T. D. Noe, Table of n, a(n) for n = 1..1000 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 Adjacent sequences: A240069 A240070 A240071 * A240073 A240074 A240075 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.)