# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a190287 Showing 1-1 of 1 %I A190287 #4 Mar 30 2012 18:57:27 %S A190287 5,4,1,3,0,8,5,6,4,5,4,1,1,0,2,8,7,1,0,2,8,7,0,6,5,5,6,7,5,5,7,4,9,4, %T A190287 1,3,5,3,1,5,9,3,2,7,3,6,5,0,4,1,2,5,8,4,1,5,5,0,5,1,3,3,7,5,9,2,2,6, %U A190287 7,7,4,4,9,2,3,3,0,9,7,1,9,2,2,5,1,8,4,8,8,1,5,1,0,0,2,8,8,0,8,8,7,4,0,9,0,0,2,2,3,2,0,9,6,8,1,4,0,4,0,2 %N A190287 Decimal expansion of (5+sqrt(25+4r))/2, where r=sqrt(5). %C A190287 The rectangle R whose shape (i.e., length/width) is (5+sqrt(25+4r))/2, where r=sqrt(5), can be partitioned into rectangles of shapes 5 and r in a manner that matches the periodic continued fraction [5, r, 5, r, ...]. R can also be partitioned into squares so as to match the nonperiodic continued fraction [5,2,2,2,1,1,1,10,1,1,2,1,...] at A190288. For details, see A188635. %e A190287 5.413085645411028710287065567557494135316... %t A190287 r=5^(1/2) %t A190287 FromContinuedFraction[{5, r, {5, r}}] %t A190287 FullSimplify[%] %t A190287 ContinuedFraction[%, 100] (* A190288 *) %t A190287 RealDigits[N[%%, 120]] (* A190287 *) %t A190287 N[%%%, 40] %Y A190287 Cf. A188635, A190288. %K A190287 nonn,cons %O A190287 1,1 %A A190287 _Clark Kimberling_, May 07 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE