A188739 Decimal expansion of e+sqrt(e^2-1).

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

Offset: 1

Author

Clark Kimberling, Apr 11 2011

Keywords

• nonn
• cons

Comments

Decimal expansion of the shape of a greater 2e-contraction rectangle; see A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and the partitioning of these rectangles into sets of squares in a manner that matches the continued fractions of their shapes.

Examples

			5.24594005277075985646114668616376972685147198530... = 1/A188738 .
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A001113, A188738 (inverse), A188627 (continued fraction), A365927.

Programs

Magma

SetDefaultRealField(RealField(100)); Exp(1) + Sqrt(Exp(2) -1); // G. C. Greubel, Nov 01 2018

Mathematica

r = 2 E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (* A188739 *)
ContinuedFraction[t, 120] (* A188627 *)
RealDigits[E+Sqrt[E^2-1],10,150][[1]] (* Harvey P. Dale, Oct 25 2020 *)

PARI

default(realprecision, 100); exp(1) + sqrt(exp(2) - 1) \\ G. C. Greubel, Nov 01 2018

Formula

e+sqrt(-1+e^2), with continued fraction A188627.

Equals exp(A365927). - Amiram Eldar, Oct 18 2023