

A308720


The maximum value in the continued fraction of sqrt(n), or 0 if there is no fractional part.


0



0, 0, 2, 2, 0, 4, 4, 4, 4, 0, 6, 6, 6, 6, 6, 6, 0, 8, 8, 8, 8, 8, 8, 8, 8, 0, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 16, 16, 16, 16, 16, 16, 16
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

The continued fraction expansion of sqrt(n) is periodic, and the maximal element is the last element in the period, 2*floor(sqrt(n)).


LINKS



FORMULA

a(k^2) = 0.
a(m) = floor(sqrt(m)) for nonsquare m.


MATHEMATICA

{0} ~Join~ Table[2 Mod[Floor@ Sqrt@ n, Ceiling@ Sqrt@ n], {n, 100}] (* Giovanni Resta, Jun 29 2019 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



