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

[Don McDonald]

In message <sCLBGvAnbNL+EwtX at borve.demon.co.uk> you write:

> 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.
> 
> ...
> Neil Fernandez
>
I presume phi = golden ratio = (sqrt(5)+1  ) / 2.

In which case it is trivial to calculate exact powers of a surd.
No, I think it is not unique?

I remember powers of (3-2V)^n -> tend to 0.
V = sqrt(2)

Higher powers ... differ negligibly from whole numbers.***
'Almost isoceles right triangles.'  (nz science monthly 1999XX.)

And 'approximations of sqrt(2).'  New Zealand mathematics magazine
2001. (Prof. John Butcher and Don McDonald.)

V2 = sqrt (2).  Yields an extremely easy integer recurrence.

I have submitted
comment A051009, eric weisstein, pythagoras's constant. To EIS.

Egyptian fraction for root2.
V2 = 1 +1/2 -1/12 -408' -470832' ...   SIGNED.
                      -------

eis has just added my A079490... NEW SEQ.

Exp(n) is closer to an integer than any previous
exp(k), 1<= k < n.
possible sequence 1 3 8 19 45 62?

I acknowledge Leroy Quet. (originator of this discussion?)  cheers.

I need to check (precision) of Pari.

(moderator Olivier ogerard. Greeting.
  Apologies for my poor/improving english sentences.
I have held back on computer printouts. Thank you.)

/ don.mcdonald
21.01.03  19:25  nzdt*.

my file
>.Calc.Profile.eisintegsq.Seqfan.ogerardMod.3-2V