A072908 - OEIS

A072908

Decimal expansion of the solution of equation log(2)-X*2^(-r)-exp(-X*r/(2^r-1)) = 0 for r = 4 . Solution is 9.96955802...

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

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

OFFSET

1,1

COMMENTS

This constant was conjectured to be the exact value for the 4-clause threshold in satisfiability Problem ( Olivier Dubois 1993).

LINKS

Table of n, a(n) for n=1..105.

O. Dubois, J. Carlier, Probabilistic approach to the satisfiability Problem, Theoretical Computer Science, 81, 1991, pp. 65-75.

MATHEMATICA

16*Log[2] + 15/4*ProductLog[-2*2^(11/15)/15] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Mar 04 2013 *)

PROG

(PARI) r=4; solve(X=9, 10, log(2)-X*2^(-r)-exp(-X*r/(2^r-1)))