ln(m)'s close to integers

[Jim Nastos]

On Sun, 19 Jan 2003, Leroy Quet wrote:

> Consider the integers m, m >= 2, such that:
> ln(m) is closer to an integer than any previous term of the sequence.
> 
> I THINK (calculated much too carelessly with a hand-calculator), that
> the sequence begins:
> 2, 3, 7, 20, ....

> Anything to add?

  A quick program confirms your values and gives:
2
3
7
20
148
403
1096
1097
2980
2981
8103
59874
162755
442413
1202604
3269017
8886110
8886111
24154952
24154953
65659969
178482301

  Which is susceptible to overflow error... I trust at least the first 15 
or so terms are correct.
  2, 3, 7, 20, 148 do not exist in the encyclopedia.

Jim Nastos