A064932 Period of the continued fraction for sqrt(3^(2n+1)).

2, 10, 30, 98, 270, 818, 2382, 7282, 21818, 65650, 196406, 589982, 1768938, 5309294, 15924930, 47779238, 143322850, 429998586, 1289970842, 3869957114, 11609762666, 34829416842, 104488103446

Offset

1,1

Comments

Limit_{n->oo} a(n)/3^n = 1.11... - A.H.M. Smeets, Oct 25 2017

References

R. K. Guy, personal communication.

Links

Table of n, a(n) for n=1..23.

Formula

a(n) = A003285(A013708(n)). - Michel Marcus, Sep 25 2019

Mathematica

Table[Length[Last[ContinuedFraction[Sqrt[3^(2n+1)] ]]], {n, 10}]

Crossrefs

Cf. A003285, A013708, A059927.

Sequence in context: A234471 A196317 A318579 * A343513 A285956 A219667

Adjacent sequences: A064929 A064930 A064931 * A064933 A064934 A064935

Keyword

hard,nonn,more

Author

Wouter Meeussen, Oct 26 2001

Extensions

a(11)-a(13) from A.H.M. Smeets, Sep 28 2017

a(14) from A.H.M. Smeets, Oct 08 2017

a(15)-a(19) from Daniel Suteu, Jan 24 2019

a(20) from Chai Wah Wu, Sep 23 2019

a(21)-a(23) from Chai Wah Wu, Sep 25 2019

Status

approved