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

[Neil Fernandez]

I wonder whether phi is unique in that every one of its powers has, as
the nearest integer to it, a term in its sequence; and no term in the
sequence is not the nearest integer to one of its powers.

phi^3 doesn't work, owing to the first, second, and fourth terms,
although for n>2 the sign of log_(phi^3)(a(n)) does alternate as n
increases.

a(n)    log_(phi^3)(a(n))

2       0.48014003
3       0.761003943     
4       0.96028006      
17      1.962554532     
18      2.002147915864
76      2.999880104602
322     4.000006680931
1364    4.999999627683
5778    6.000000020749
24476   6.999999998844
103682  8.000000000064

Neil

-- 
Neil Fernandez