Sequence generated by egyptian fractions and the greedy algorithm

[Neil Sloane]

here is a message to seqfans

My colleague R. L. Graham mentioned a nice new
source for sequences.

Many variations are possible.  Here is a simple version.

Take a number, say 3

This produces a sequence as follows:

We try to write 1 / 3 as a sum

1/3 = 1/a^2 + 1/b^2 + 1/c^2 + 1/d^2 + ...

where we use the greedy algorithm to find a, b, c, ...

Then the sequence is a,b,c,d,...

We get a=2, b=4, c=7, d=49 (i think)

It isn't known if such sequences are finite or infinite.

If any readers would care to generate such sequences
it would be nice to have them in the data base


Neil


 Neil J. A. Sloane, njas at research.att.com,
 Note new address: AT&T Research Labs, Room C233, 180 Park Ave,
 Florham Park, NJ 07932-0971 USA.
 Home page: http://www.research.att.com/~njas/
 Office phone: (973) 360 8415; fax: (973) 360 8178
 My home number has also changed, to (732) 828 6098