A188935 - OEIS

%I #14 Jul 04 2023 03:27:55

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

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

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

%N Decimal expansion of (1+sqrt(37))/6.

%C Decimal expansion of the length/width ratio of a (1/3)-extension rectangle.  See A188640 for definitions of shape and r-extension rectangle.

%C A (1/3)-extension rectangle matches the continued fraction [1,5,1,1,5,1,1,5,1,1,5,...] for the shape L/W=(1+sqrt(37))/6.  This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...].  Specifically, for the (1/3)-extension rectangle, 1 square is removed first, then 5 squares, then 1 square, then 1 square,..., so that the original rectangle of shape (1+sqrt(37))/6 is partitioned into an infinite collection of squares.

%F Equals exp(arcsinh(1/6)). - _Amiram Eldar_, Jul 04 2023

%e 1.1804604217163699481666140408670111770141616824644...

%t RealDigits[(1 + Sqrt[37])/6, 10, 111][[1]] (* _Robert G. Wilson v_, Aug 18 2011 *)

%Y Cf. A188640, A188934.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Apr 13 2011