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 A190177 Decimal expansion of (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2. 5
 3, 1, 7, 4, 6, 7, 3, 8, 9, 4, 0, 3, 4, 1, 9, 8, 9, 2, 2, 9, 5, 8, 0, 7, 4, 4, 1, 2, 2, 1, 7, 2, 4, 3, 6, 4, 2, 9, 7, 4, 7, 8, 6, 1, 5, 8, 4, 1, 2, 1, 9, 6, 8, 7, 2, 9, 8, 3, 9, 9, 1, 1, 8, 5, 4, 1, 0, 0, 5, 5, 6, 5, 1, 4, 4, 6, 7, 5, 0, 7, 8, 7, 0, 3, 2, 2, 7, 3, 6, 2, 7, 3, 8, 2, 3, 0, 1, 0, 0, 7, 3, 9, 0, 6, 8, 1, 8, 5, 8, 2, 5, 9, 5, 1, 7, 6, 4, 3, 9, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let R denote a rectangle whose shape (i.e., length/width) is (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2.  R can be partitioned into squares and silver rectangles in a manner that matches the periodic continued fraction [r,1,r,1,r,1,r,1,...], where r is the silver ratio: 1+sqrt(2)=[2,2,2,2,2,...].  R can also be partitioned into squares so as to match the nonperiodic continued fraction [3,5,1,2,1,1,1,2,...] at A190178.  For details, see A188635. LINKS EXAMPLE 3.174673894034198922958074412217243642975... MATHEMATICA r = 1 + 2^(1/2)); FromContinuedFraction[{r, 1, {r, 1}}] FullSimplify[%] ContinuedFraction[%, 100]  (* A190178 *) RealDigits[N[%%, 120]]     (* A190177 *) N[%%%, 40] CROSSREFS Cf. A188635, A190178, A189970, A190179. Sequence in context: A158841 A213576 A021319 * A283764 A010603 A269423 Adjacent sequences:  A190174 A190175 A190176 * A190178 A190179 A190180 KEYWORD nonn,cons AUTHOR Clark Kimberling, May 05 2011 STATUS approved

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