A196396 Decimal expansion of the positive number x satisfying e^x=2*cos(x).

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

Offset

0,1

Links

Table of n, a(n) for n=0..100.

Example

0.539785160809281104845589159774383394929526709...

Mathematica

Plot[{E^x, 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, Pi/2}]
t = x /.
  FindRoot[E^x == 2 Cos[x], {x, .5, .6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196396 *)
t = x /.
  FindRoot[E^x == 3 Cos[x], {x, .7, .8}, WorkingPrecision -> 100]; RealDigits[t]  (* A196397 *)
t = x /.
  FindRoot[E^x == 4 Cos[x], {x, .8, 1.0}, WorkingPrecision -> 100]; RealDigits[t]  (* A196398 *)
t = x /.
  FindRoot[E^x == 5 Cos[x], {x, .8, 1.0}, WorkingPrecision -> 100]; RealDigits[t]  (* A196399 *)
t = x /.
  FindRoot[E^x == 6 Cos[x], {x, 1.0, 1.1}, WorkingPrecision -> 100]; RealDigits[t]  (* A196400 *)

Crossrefs

Cf. A196401, A196407.

Sequence in context: A118273 A242616 A073891 * A086970 A224511 A201938

Adjacent sequences: A196393 A196394 A196395 * A196397 A196398 A196399

Keyword

nonn,cons

Author

Clark Kimberling, Oct 02 2011

Extensions

a(100) corrected by Georg Fischer, Jul 30 2021

Status

approved