a possibly new sequence?

[Rob Pratt]

The problem can be thought of as finding a maximum independent set in a
graph with node set {1, 2, ..., N} and an edge (i, j) if |i - j| is a
square.

First 100 terms (computed using integer programming formulation):
1,1,2,2,2,3,3,4,4,4,5,5,6,6,6,7,7,8,8,8,9,9,10,10,10,10,10,10,10,10,10,1
0,10,10,11,11,11,12,12,12,12,12,13,13,13,13,13,14,14,14,14,14,15,15,15,1
5,15,16,16,16,16,16,16,16,16,17,17,18,18,18,19,19,20,20,20,20,20,20,20,2
0,21,21,21,21,21,22,22,22,22,22,22,23,23,23,23,23,24,24,24,24

This sequence does not seem to be in the OEIS.

Rob

-----Original Message-----
From: N. J. A. Sloane [mailto:njas at research.att.com] 
Sent: Monday, September 17, 2007 10:04 AM
To: seqfan at ext.jussieu.fr
Cc: njas at research.att.com
Subject: a possibly new sequence?


This was posted to the number theory list - could someone work out the
first few terms
and see if it is a new sequence?   Neil

Date:         Mon, 17 Sep 2007 09:09:06 -0400
Reply-To: Sujith Vijay <sujith at EDEN.RUTGERS.EDU>
From: Sujith Vijay <sujith at EDEN.RUTGERS.EDU>

What bounds are known for the size of the largest subset of {1,2,...,N}
s uch that no two distinct elements differ by a perfect square? 

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