A066724 - OEIS

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 #15 Feb 26 2022 21:05:55

%S 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 67,71,73,79,81,83,84,89,97,101,103,107,109,113,121,127,128,131,137,

%U 139,149,151,154,157,163,167,169,173,179,180,181,191,193,197,199,211

%N 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 The first 15 terms are the same as A026477; the first 13 terms are the same as A026416.

%C Contains all primes. - _Ivan Neretin_, Mar 02 2016

%H Ivan Neretin, <a href="/A066724/b066724.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 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 Cf. A000028, A026477, A026416, A050376, A084400.

%Y Cf. A080431, A066720.

%K easy,nonn

%O 1,2

%A Robert E. Sawyer (rs.1(AT)mindspring.com), Jan 18 2002