A059648

[karttu at megabaud.fi]

Hmm, it seems that again I have made a public ass of myself.
Any fifth grader could tell you why the difference
  [(k^2)*n]-(k*[k*n])
gets only non-negative values when k is a square root of
a non-square integer. Furthermore, I almost see why k = (sqrt(5)+1)/2
(or some of its powers), is the only non SQRT(D) value for which this
holds also. Indeed, this was just another example of "turn computer on,
brain off" syndrome which affects me. Also, I should add a lock to my
mailing program, which would forbid sending mail after midnight.

So, Neil, please remove the "Problem" and "Conjecture" from A059648.
Still, some of the "almost periodic" (quasi-periodic?) sequences arising
as first differences of such sequences could be interesting.


Terveisin,

  Antti Karttunen