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

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

Mathematica

a[n_] := If[IntegerQ[Sqrt[n]], 1, Length[ContinuedFraction[Sqrt[n]][[2]]]];
Table[a[n], {n, 1, 103}] (* Jean-François Alcover, Jan 09 2025 *)

Crossrefs

See A003285, which is the main entry for this sequence.

Sequence in context: A297170 A359627 A127309 * A160266 A322134 A023504

Adjacent sequences: A097850 A097851 A097852 * A097854 A097855 A097856

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 01 2004

Status

approved