A062345 Length of period of continued fraction expansion of square root of 3^n-1.

1, 2, 1, 2, 10, 2, 19, 2, 25, 2, 156, 2, 149, 2, 580, 2, 716, 2, 6461, 2, 2485, 2, 123256, 2, 64, 2, 8638, 2, 722190, 2, 3804214, 2, 1783536, 2, 3550696, 2, 86022946, 2, 22119349, 2, 692630166, 2, 8247763078, 2, 43380360, 2, 15150768502, 2, 10229872316, 2, 36580802370, 2, 333495606762, 2, 676122216162, 2

Offset: 1

Author

Labos Elemer, Jul 13 2001

Keywords

• nonn
• more

Examples

			The period of sqrt(242) contains 10 terms: [1,1,3,1,14,1,3,1,1,30]
		

Crossrefs

Cf. A003285, A024023, A059866, A059926, A059927, A062328.

Programs

Maple

with(numtheory): [seq(nops(cfrac(sqrt(3^k-1),'periodic','quotients')[2]),k=1..16)];

Mathematica

Table[Length[Last[ContinuedFraction[Sqrt[ -1+3^u]]]], {u, 1, 36}]

Formula

a(n) = A003285(A024023(n)). - Michel Marcus, Sep 25 2019

Extensions

a(37)-a(42) from Vaclav Kotesovec, Aug 28 2019

a(43)-a(44) from Vaclav Kotesovec, Sep 17 2019

a(45)-a(52) from Chai Wah Wu, Sep 25 2019

a(53)-a(56) from Chai Wah Wu, Sep 29 2019