A064849 Period of continued fraction for sqrt(3)*n.

2, 2, 2, 2, 4, 8, 2, 4, 10, 4, 2, 8, 6, 2, 2, 8, 6, 20, 4, 8, 14, 8, 8, 12, 16, 2, 30, 2, 16, 4, 18, 16, 10, 20, 16, 20, 18, 8, 6, 12, 2, 12, 8, 8, 6, 20, 20, 20, 30, 36, 6, 2, 8, 68, 14, 2, 16, 32, 22, 4, 38, 18, 40, 36, 6, 28, 10, 20, 40, 8, 4, 40, 18, 22, 16, 12, 28, 2, 46, 20, 98, 8

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

A040001 (cfrac for n=1) has period length 2, so a(1)=2. A040008 (cfrac for n=2) has period length 2, so a(2)=2. A040021 (cfrac for =3) has period length 2, so a(3)=2. - R. J. Mathar, Feb 10 2016

Maple

f:= proc(n) uses NumberTheory;
   nops(Term(ContinuedFraction(sqrt(3)*n), periodic)[2])
end proc:
map(f, [$1..100]); # Robert Israel, Apr 14 2026

Mathematica

Table[Length[Last[ContinuedFraction[Sqrt[3] n]]], {n, 128}]

Crossrefs

Cf. A064848, A064850, A064851, A064860, A064862, A064863, A064864, A064887, A064897, A064912.

Sequence in context: A334125 A364811 A244459 * A269302 A132189 A162799

Adjacent sequences: A064846 A064847 A064848 * A064850 A064851 A064852

Keyword

nonn

Author

R. K. Guy, Oct 26 2001

Status

approved