

A188739


Decimal expansion of e+sqrt(e^21).


7



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000


FORMULA

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


EXAMPLE

5.24594005277075985646114668616376972685147198530... = 1/A188738 .


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^21], 10, 150][[1]] (* Harvey P. Dale, Oct 25 2020 *)


PROG

(PARI) default(realprecision, 100); exp(1) + sqrt(exp(2)  1) \\ G. C. Greubel, Nov 01 2018
(MAGMA) SetDefaultRealField(RealField(100)); Exp(1) + Sqrt(Exp(2) 1); // G. C. Greubel, Nov 01 2018


CROSSREFS

Cf. A188738 (inverse), A188627 (continued fraction).
Sequence in context: A266122 A064853 A177148 * A308171 A265287 A329477
Adjacent sequences: A188736 A188737 A188738 * A188740 A188741 A188742


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Apr 11 2011


STATUS

approved



