cp's OEIS Frontend

A066724 a(1) = 1, a(2) = 2; 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.

%I A066724 #15 Feb 26 2022 21:05:55
%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, a(2) = 2; 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.
%C A066724 Contains all primes. - _Ivan Neretin_, Mar 02 2016
%H A066724 Ivan Neretin, <a href="/A066724/b066724.txt">Table of n, a(n) for n = 1..1000</a>
%e A066724 a(7) is not 10 because we already have 10 = 2*5. Of course all primes appear. a(14) is not 24 because if it were there would be a repeat among the terms a(i)*a(j) for 1 <= i < j <= 14, namely 3*16 = 2*24.
%t A066724 f[l_List] := Block[{k = 1, p = Times @@@ Subsets[l, {2}]},While[Intersection[p, l*k] != {}, k++ ];Append[l, k]];Nest[f, {1, 2}, 62] (* _Ray Chandler_, Feb 12 2007 *)
%Y A066724 Cf. A000028, A026477, A026416, A050376, A084400.
%Y A066724 Cf. A080431, A066720.
%K A066724 easy,nonn
%O A066724 1,2
%A A066724 Robert E. Sawyer (rs.1(AT)mindspring.com), Jan 18 2002