A103555 Decimal expansion of solution to x*10^x=1.

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

Offset: 0

Author

Zak Seidov, Mar 23 2005

Keywords

• nonn
• cons

Programs

Maple

read("transforms3") ; Digits := 120 ; x := 0.4 ; for l from 1 to 10 do x := x-(x-10^(-x))/(1+x*log(10)) : x := evalf(x) ; end do; CONSTTOLIST(x) ; # R. J. Mathar, Mar 23 2010

Mathematica

RealDigits[x/.FindRoot[x 10^x==1,{x,.39},WorkingPrecision->150]][[1]] (* Harvey P. Dale, Jun 21 2012 *)
RealDigits[ ProductLog[Log[10]] / Log[10], 10, 105][[1]] (* Jean-François Alcover, Jan 28 2014 *)

PARI

solve(x=0,1,x*10^x-1) \\ Charles R Greathouse IV, Jun 08 2015

Formula

x = 0.3990129782602520715964708106240920239962... ; x*10^x=1.

Extensions

More digits from R. J. Mathar, Mar 23 2010