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 A188885 Decimal expansion of (1+sqrt(1+e^2))/e. 1
 1, 4, 3, 3, 4, 0, 0, 5, 7, 3, 4, 0, 5, 1, 5, 4, 8, 4, 6, 3, 3, 1, 9, 0, 6, 9, 1, 9, 9, 7, 6, 7, 5, 2, 3, 2, 8, 8, 4, 3, 3, 9, 1, 1, 8, 3, 9, 5, 3, 6, 7, 0, 7, 8, 9, 8, 2, 5, 7, 9, 4, 6, 7, 9, 5, 0, 7, 5, 2, 7, 3, 9, 3, 9, 0, 5, 2, 7, 0, 6, 8, 9, 7, 5, 0, 7, 3, 6, 9, 7, 8, 9, 0, 9, 2, 5, 4, 5, 6, 5, 0, 5, 7, 4, 3, 2, 9, 4, 0, 8, 7, 5, 5, 5, 9, 0, 7, 4, 4, 7, 4, 8, 2, 3, 5, 3, 9, 4, 0, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Decimal expansion of the length/width ratio of a (2/e)-extension rectangle.  See A188640 for definitions of shape and r-extension rectangle. A (2/e)-extension rectangle matches the continued fraction [1,2,3,3,1,15,1,3,7,1,2,4,...] for the shape L/W=(1+sqrt(1+e^2))/e.  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 (2/e)-extension rectangle, 1 square is removed first, then 2 squares, then 3 square2, then 3 squares,..., so that the original rectangle of shape (1+sqrt(1+e^2))/e is partitioned into an infinite collection of squares. LINKS EXAMPLE 1.433400573405154846331906919976752328843391... MATHEMATICA r = 2/E; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] N[t, 130] RealDigits[N[t, 130]][[1]] ContinuedFraction[t, 120] CROSSREFS Cf. A188640, A188886. Sequence in context: A282445 A281705 A026858 * A129344 A048853 A303701 Adjacent sequences:  A188882 A188883 A188884 * A188886 A188887 A188888 KEYWORD nonn,cons AUTHOR Clark Kimberling, Apr 12 2011 STATUS approved

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Last modified January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)