This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A190179 Decimal expansion of (1+sqrt(-3+4*sqrt(2)))/2. 5
 1, 3, 1, 4, 9, 9, 2, 9, 8, 3, 0, 2, 0, 7, 7, 1, 1, 9, 7, 1, 1, 9, 1, 6, 4, 2, 0, 3, 6, 3, 8, 2, 6, 3, 0, 4, 4, 5, 6, 4, 9, 0, 9, 3, 4, 6, 6, 3, 3, 7, 5, 6, 0, 0, 3, 2, 0, 8, 0, 0, 3, 1, 7, 2, 6, 0, 5, 6, 0, 2, 8, 8, 6, 5, 3, 6, 0, 3, 8, 8, 6, 6, 1, 9, 2, 6, 2, 4, 0, 6, 2, 5, 8, 0, 8, 8, 0, 9, 3, 2, 4, 8, 0, 9, 9, 1, 8, 4, 8, 1, 5, 5, 0, 8, 9, 5, 5, 3, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let R denote a rectangle whose shape (i.e., length/width) is (1+sqrt(-3+4*sqrt(2)))/2.  R can be partitioned into squares and silver rectangles in a manner that matches the periodic continued fraction [1,r,1,r,...], 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 [1,3,5,1,2,1,1,1,2,...] at A190180.  For details, see A188635. The real value a-1 is the only invariant point of the complex-plane mapping M(c,z)=sqrt(c-sqrt(c+z)), with c = sqrt(2), and its only attractor, convergent from any starting complex-plane location. - Stanislav Sykora, Apr 29 2016 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10001 FORMULA Equals 1+sqrt(c-sqrt(c+sqrt(c-sqrt(c+ ...)))), with c=sqrt(2). - Stanislav Sykora, Apr 29 2016 EXAMPLE 1.314992983020771197119164203638263044565... MATHEMATICA r = 1 + 2^(1/2)); FromContinuedFraction[{1, r, {1, r}}] FullSimplify[%] ContinuedFraction[%, 100]  (* A190180 *) RealDigits[N[%%, 120]]     (* A190179 *) N[%%%, 40] RealDigits[(1+Sqrt[4Sqrt[2]-3])/2, 10, 120][[1]]  Harvey P. Dale, May 19 2012 PROG (PARI) (1+sqrt(-3+4*sqrt(2)))/2 \\ Altug Alkan, Apr 29 2016 CROSSREFS Cf. A188635, A190180, A190177, A190178. Sequence in context: A202353 A108621 A193792 * A025116 A178300 A081720 Adjacent sequences:  A190176 A190177 A190178 * A190180 A190181 A190182 KEYWORD nonn,cons AUTHOR Clark Kimberling, May 05 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 01:33 EST 2017. Contains 295954 sequences.