request for help in understanding a new sequence (163 line message)

[Max A.]

On 9/26/06, N. J. A. Sloane <njas at research.att.com> wrote:

> This is what the sequence looks like when formatted as a triangle:
> x)
> 0) 2, 3, 5, 7, 11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
> 1) 3, 4, 6, 8, 12,14,18,20,24,30,32,38,42,44,48,54,60,62,68,72,74,80,84,90,98,
> 2) 5, 6, 7, 9, 13,15,19,21,25,31,33,39,43,45,49,55,61,63,69,73,75,81,85,91,99,

I believe the x-th row (x=0,1,2,...) contains those positive integers
n for which
a multiset { n mod k : k=2,3,...,n } contains exactly one copy of x.

For example, the 0-th row obviously contains all prime numbers.

In general, the x-th row contains all numbers n>2x such that n-x does
not have divisors d with x < d < n-x. In other words, if p is the
smallest prime divisor of n-x then (n-x)/p <= x.

Max