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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.)