# puzzling sequence

N. J. A. Sloane njas at research.att.com
Fri Dec 5 12:35:46 CET 2003

```Dear Seqfans,  There are several sequences which appear identical
to A000028, and I am trying to clear them up.
Can anyone understand the following sequence?

%I A066724
%S A066724 1,2,3,4,5,7,9,11,13,16,17,19,23,25,29,30,31,37,41,43,47,49,53,59,61,
%T A066724 67,71,73,79,81,83,84,89,97,101,103,107,109,113,121,127,128,131,137,
%U A066724 139,149,151,154,157,163,167,169,173,179,180,181,191,193,197,199,211
%N A066724 a(1) = 1; for n > 1, a(n) is the least integer > a(n-1) such that the products a(i)*a(j), for 1 <= i < j <= n, are all distinct.
%C A066724 The first 15 terms are the same as A026477; the first 13 terms are the same as A026416.
%Y A066724 Cf. A026477, A026416.
%Y A066724 Adjacent sequences: A066721 A066722 A066723 this_sequence A066725 A066726 A066727
%Y A066724 Sequence in context: A026416 A026418 A000028 this_sequence A009087 A026477 A050376
%K A066724 easy,nonn
%O A066724 1,2
%A A066724 Robert E. Sawyer (rs.1(AT)mindspring.com), Jan 18 2002

My question is, why is 24 missing?

Superficially the description is identical to that of A026416 and A000028
(which really are the same except that A026416 has an initial 1)
and A026418 (which has now been deleted)

I suspect that A066724 is generated by a slightly different rule than
what it says, but what?

Neil Sloane.

```