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

Author

Labos Elemer, Mar 01 2001

Keywords

• nonn
• nice
• more

Comments

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

Crossrefs

Cf. A003285, A059866, A059926, A087289.

Programs

Mathematica

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

Formula

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

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