A190289 - OEIS

%I #6 Dec 13 2019 16:29:57

%S 1,8,9,5,6,4,3,9,2,3,7,3,8,9,6,0,0,0,1,6,4,7,0,1,1,7,9,8,4,3,2,0,0,2,

%T 1,2,2,2,4,6,1,1,4,1,4,4,1,9,1,9,9,2,9,7,5,6,5,1,8,1,0,5,3,0,9,7,6,7,

%U 1,7,1,0,6,3,8,6,9,4,2,7,2,1,6,5,1,0,9,0,3,8,9,8,7,3,3,6,1,2,5,8,1,6,9,4,0,0,2,2,6,3,4,9,3,9,6,4,3,5,2,1

%N Decimal expansion of (3+sqrt(21))/4.

%C The rectangle R whose shape (i.e., length/width) is (3+sqrt(21))/4, can be partitioned into rectangles of shapes 3/2 and 2 in a manner that matches the periodic continued fraction [3/2, 2, 3/2, 2,  ...].  R can also be partitioned into squares so as to match the periodic continued fraction [1,1,8,1,1,2,1,1,8,1,1,2,,...].  For details, see A188635.

%e 1.895643923738960001647011798432002122246...

%t FromContinuedFraction[{3/2, 2, {3/2, 2}}]

%t ContinuedFraction[%, 100]  (* [1,1,8,1,1,2,... *)

%t RealDigits[N[%%, 120]]     (* A190289 *)

%t N[%%%, 40]

%t RealDigits[(3+Sqrt[21])/4,10,120][[1]] (* _Harvey P. Dale_, Dec 13 2019 *)

%Y A188635.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, May 07 2011