A097853 - OEIS

A097853

Period of continued fraction for square root of n (or 1 if n is a square).

1, 1, 2, 1, 1, 2, 4, 2, 1, 1, 2, 2, 5, 4, 2, 1, 1, 2, 6, 2, 6, 6, 4, 2, 1, 1, 2, 4, 5, 2, 8, 4, 4, 4, 2, 1, 1, 2, 2, 2, 3, 2, 10, 8, 6, 12, 4, 2, 1, 1, 2, 6, 5, 6, 4, 2, 6, 7, 6, 4, 11, 4, 2, 1, 1, 2, 10, 2, 8, 6, 8, 2, 7, 5, 4, 12, 6, 4, 4, 2, 1, 1, 2, 2, 5, 10, 2, 6, 5, 2, 8, 8, 10, 16, 4, 4, 11, 4, 2, 1, 1, 2, 12

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..103.

EXAMPLE

1 is a square. 2 has continued fraction [1;2,2,2...], 3 has [1;1,2,1,2,1,2...]. - Georg Fischer, Jun 14 2019

MAPLE

a:= n-> `if`(issqr(n), 1, nops(numtheory[cfrac](

sqrt(n), 'periodic', 'quotients')[2])):

seq(a(n), n=1..120); # Alois P. Heinz, Jun 14 2019

CROSSREFS