A061682 Length of period of continued fraction expansion of square root of (2^(2n+1)+1).

4, 10, 16, 44, 74, 46, 204, 714, 702, 908, 404, 7754, 1136, 9886, 8154, 23578, 65096, 404762, 23992, 3514774, 110124, 4802160, 6490450, 180832, 115972, 770304, 62665998, 133093360, 1019300318, 60079334, 113987888, 5702124038, 4463754028, 713372392, 38574516706, 9096543466, 7030527700, 582442851838, 16708770664, 32628786870

Offset

2,1

Comments

Old definition was: "Quotient cycle length in continued fraction expansion of sqrt(2^(2n+1)+1)."

Links

Table of n, a(n) for n=2..41.

Formula

a(n) = A003285(A087289(n)). - Michel Marcus, Sep 26 2019

Mathematica

a[n_] := ContinuedFraction[Sqrt[2^(2n+1)+1]] // Last // Length; Table[a[n], {n, 2, 28}] (* Jean-François Alcover, Dec 11 2016 *)

Crossrefs

Cf. A003285, A059866, A059926, A087289.

Sequence in context: A025621 A056486 A233452 * A246882 A038240 A369613

Adjacent sequences: A061679 A061680 A061681 * A061683 A061684 A061685

Keyword

nonn,nice,more

Author

Labos Elemer, Mar 01 2001

Extensions

One more term from David W. Wilson, Jun 18 2001

Corrected and extended by Naohiro Nomoto, Nov 09 2001

a(29)-a(31) from Daniel Suteu, Jan 25 2019

a(32) from Chai Wah Wu, Sep 23 2019

a(33)-a(38) from Chai Wah Wu, Sep 25 2019

Simpler definition from Bernard Schott, Sep 26 2019

a(39)-a(41) from Chai Wah Wu, Sep 29 2019

Status

approved