A059866 Period of the continued fraction for sqrt(2^n-1).

2, 4, 2, 8, 2, 12, 2, 20, 2, 12, 2, 164, 2, 40, 2, 40, 2, 1208, 2, 660, 2, 1304, 2, 3056, 2, 2492, 2, 1080, 2, 13004, 2, 10232, 2, 11296, 2, 148736, 2, 56576, 2, 615482, 2, 44448, 2, 64, 2, 2628524, 2, 28219952, 2, 139558, 2, 3067080, 2, 2683626, 2, 90740360, 2, 103050292, 2

Offset

2,1

Links

Chai Wah Wu, Table of n, a(n) for n = 2..78

Example

For n=7 and n=8 the continued fractions are [[11], [3, 1, 2, 2, 7, 11, 7, 2, 2, 1, 3, 22]] and [[15], [1, 30]] with periods 12 and 2, respectively.

Maple

with(numtheory): [seq(nops(cfrac(sqrt(2^k-1), 'periodic', 'quotients')[2]), k=2..30)];

Mathematica

Table[Length@ Last@ ContinuedFraction[Sqrt[2^n - 1]], {n, 2, 56}] (* Michael De Vlieger, Mar 21 2015 *)

Crossrefs

Cf. A003285, A059926, A059927, A064932.

Sequence in context: A307669 A171977 A266073 * A278262 A093895 A030057

Adjacent sequences: A059863 A059864 A059865 * A059867 A059868 A059869

Keyword

nonn

Author

Labos Elemer, Feb 28 2001

Extensions

Corrected and extended by Naohiro Nomoto, Nov 09 2001

a(57)-a(60) from Daniel Suteu, Jan 25 2019

Status

approved