log(m)'s close to integers, various log bases

[Jim Nastos]

On Tue, 21 Jan 2003, Neil Fernandez wrote:

> Phi gives
> 2, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207,
> 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443,
> 439204, 710647
<snip>
> For phi: 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1,
> 1, -1, 1, -1, 1, -1, 1, -1, 1
> 
> Does the phi sequence ever stop alternating between 1 and -1?

  Yes, it seems to stop alternating on the 35th term:

3 +
4 -
7 +
11 -
18 +
29 -
47 +
76 -
123 +
199 -
322 +
521 -
843 +
1364 -
2207 +
3571 -
5778 +
9349 -
15127 +
24476 -
39603 +
64079 -
103682 +
167761 -
271443 +
439204 -
710647 +
1149851 -
1860498 +
3010349 -
4870847 +
7881196 -
12752043 +
20633239 +

  Interesting other questions. The first question I asked myself was "are 
these sequences always infinite?" ... after a moment's thought, it was 
obvious :)

Jim Nastos