A question about A079490

[Mark Hudson]

Hi all,

I have a question about sequence A079490.

ID Number: A079490
Sequence:  1,3,8,19,45,62
Name:      Exp(n) is closer to an integer than any previous exp(k) for 1 <= 
k < n.
Example:   a(2) = 3, exp(3) = 20.08... is closer to an integer than exp(1) = 
2.718...
Program:   (PARI) d=1; for( n=1,500, x=exp(n); y=1/(( x-floor(x)) *
              (ceil(x)-x)) ; if( y>d, print( n); d= y, ))

I was thinking of extending the sequence when I ran into a question.

The terms I get are:

1,3,8,19,45,75,135,178,209,732,...

so my sequence diverges from the one in the database after term=45.

If my understanding of the definition of the sequence is correct, then I 
should look at the fractional parts of exp(n) for each term:

frac(exp(45)) = 0.03479...
frac(exp(62)) = 0.0373...
frac(exp(75)) = 0.01434...

Although I may have missed a term before 75 which is closer to its nearest 
integer than 45 is, since exp(62)) is further from an integer than exp(45) 
is, I do not see that this can be the next term in the sequence after 45.

Mark.






_________________________________________________________________
Express yourself with cool emoticons http://messenger.msn.co.uk