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A190180 Continued fraction of (1+sqrt(-3+4*sqrt(2)))/2. 3
1, 3, 5, 1, 2, 1, 1, 1, 2, 1, 12, 1, 5, 1, 1, 2, 1, 14, 2, 9, 11, 1, 12, 1, 2, 1, 832, 1, 2, 2, 5, 1, 1, 17, 1, 2, 1, 9, 1, 12, 1, 1, 1, 6, 3, 2, 1, 1, 6, 3, 1, 1, 1, 2, 2, 1, 3, 1, 3, 3, 1, 2, 1, 45, 1, 1, 1, 1, 62, 9, 1, 1, 2, 3, 1, 6, 1, 3, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equivalent to the periodic continued fraction [1,r,1,r,...] where r=1+sqrt(2), the silver ratio. For geometric interpretations of both continued fractions, see A189979 and A188635.

1 followed by A190178.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

MATHEMATICA

r = 1 + 2^(1/2));

FromContinuedFraction[{1, r, {1, r}}]

FullSimplify[%]

ContinuedFraction[%, 100]  (* A190180 *)

RealDigits[N[%%, 120]]     (* A190179 *)

N[%%%, 40]

ContinuedFraction[(1 + Sqrt[-3 + 4*Sqrt[2]])/2, 100] (* G. C. Greubel, Dec 28 2017 *)

PROG

(PARI) contfrac((1+sqrt(-3+4*sqrt(2)))/2) \\ G. C. Greubel, Dec 28 2017

(MAGMA) ContinuedFraction((1+Sqrt(-3+4*Sqrt(2)))/2); // G. C. Greubel, Dec 28 2017

CROSSREFS

Cf. A190179, A188635, A190177, A190178.

Sequence in context: A141707 A329593 A263490 * A190178 A010261 A281494

Adjacent sequences:  A190177 A190178 A190179 * A190181 A190182 A190183

KEYWORD

nonn,cofr

AUTHOR

Clark Kimberling, May 05 2011

STATUS

approved

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Last modified November 23 16:18 EST 2020. Contains 338590 sequences. (Running on oeis4.)