A196553 Decimal expansion of the number x satisfying x*2^x=6.

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

Offset

1,2

Links

Table of n, a(n) for n=1..100.

Example

x=1.765161948256699137185055703286465281800...

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[ 6*Log[2] ] / Log[2], 10, 100] // First (* Jean-François Alcover, Feb 27 2013 *)

Crossrefs

Sequence in context: A094961 A069814 A198816 * A244921 A372951 A334380

Adjacent sequences: A196550 A196551 A196552 * A196554 A196555 A196556

Keyword

nonn,cons

Author

Clark Kimberling, Oct 03 2011

Extensions

Digits from a(94) on corrected by Jean-François Alcover, Feb 27 2013

Status

approved