A190282 Continued fraction of (1+sqrt(1+r))/r, where r=sqrt(2).

1, 1, 4, 6, 1, 2, 2, 2, 1, 1, 6, 1, 179, 46, 1, 1, 3, 2, 1, 1, 3, 6, 3, 1, 1, 1, 1, 2, 1, 1, 56, 1, 1, 1, 1, 66, 1, 1, 2, 17, 8, 2, 7, 12, 1, 1, 8, 1, 2, 2, 1, 1, 2, 1, 12, 1, 2, 2, 2, 2, 1, 1, 1, 8, 1, 1, 1, 1, 2, 1, 2, 5, 1, 6, 8, 1, 1, 1, 2, 7, 1, 9, 1, 2, 5, 7, 1, 6, 1, 10, 1

Offset

0,3

Comments

Equivalent to the periodic continued fraction [r,2,r,2,...] where r=sqrt(2). For geometric interpretations of both continued fractions, see A190281 and A188635.

Links

G. C. Greubel, Table of n, a(n) for n = 0..4999

Formula

a(n) = A154748(n+2). - Georg Fischer, Oct 14 2018

Mathematica

ContinuedFraction[(1 + Sqrt[1 + Sqrt[2]])/Sqrt[2], 50] (* G. C. Greubel, Jan 31 2018 *)

Prog

(PARI) contfrac((1 + sqrt(1 + sqrt(2)))/sqrt(2)) \\ G. C. Greubel, Jan 31 2018
(Magma) ContinuedFraction((1 + Sqrt(1 + Sqrt(2)))/Sqrt(2)); // G. C. Greubel, Jan 31 2018

Crossrefs

Cf. A154748, A188635, A190281 (decimal expansion).

Sequence in context: A395934 A384213 A154748 * A164833 A248938 A106144

Adjacent sequences: A190279 A190280 A190281 * A190283 A190284 A190285

Keyword

nonn,cofr

Author

Clark Kimberling, May 07 2011

Extensions

Offset set to 0 by Andrew Howroyd, Nov 25 2025

Status

approved