

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



KEYWORD

nonn


AUTHOR



STATUS

approved



