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.

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, 67, 71, 73, 79, 81, 83, 84, 89, 97, 101, 103, 107, 109, 113, 121, 127, 128, 131, 137, 139, 149, 151, 154, 157, 163, 167, 169, 173, 179, 180, 181, 191, 193, 197, 199, 211

Offset

1,2

Comments

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

Contains all primes. - Ivan Neretin, Mar 02 2016

Links

Ivan Neretin, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

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 *)

Crossrefs

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

Cf. A080431, A066720.

Sequence in context: A026416 A123193 A345944 * A089237 A352870 A009087

Adjacent sequences: A066721 A066722 A066723 * A066725 A066726 A066727

Keyword

easy,nonn

Author

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

Status

approved