A240072 Least number k with continued fraction of sqrt(k) having periodic part of length 2*n.

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

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