A196549 Decimal expansion of the number x satisfying x*2^x=e.

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

Offset

1,3

Links

Table of n, a(n) for n=1..102.

Example

x=1.19078368297329591531800250685857010...

Mathematica

Plot[{2^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
t = x /. FindRoot[2^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A104748 *)
t = x /. FindRoot[2^x == E/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196549 *)
t = x /. FindRoot[2^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196550 *)
t = x /. FindRoot[2^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196551 *)
t = x /. FindRoot[2^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196552 *)
t = x /. FindRoot[2^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196553 *)
RealDigits[ ProductLog[ E*Log[2] ] / Log[2], 10, 100] // First (* Jean-François Alcover, Feb 27 2013 *)

Crossrefs

Cf. A196515.

Sequence in context: A363368 A097674 A309823 * A173164 A298743 A181446

Adjacent sequences: A196546 A196547 A196548 * A196550 A196551 A196552

Keyword

nonn,cons

Author

Clark Kimberling, Oct 03 2011

Status

approved