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

Author

T. D. Noe, Apr 04 2014

Keywords

• nonn

Comments

It appears that, in general, these numbers are less than the corresponding numbers for the odd lengths, A062769.

Examples

			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}.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A013646 (even and odd), A062769 (similar, but odd length).

Programs

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