A080431 -id:A080431 - 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.

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

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

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

			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.

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

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

Cf. A080431, A066720.

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 *)

A080432 Even numbers such that all a(i) + a(j) are distinct.

Original entry on oeis.org

2, 4, 6, 10, 16, 26, 42, 60, 78, 106, 148, 190, 256, 304, 364, 424, 516, 632, 748, 826, 952, 1062, 1092, 1216, 1434, 1596, 1724, 1930, 2120, 2322, 2614, 2772, 2870, 3112, 3444, 3668, 3868, 4116, 4522, 4994, 5398, 5748, 6122, 6394, 6664, 7258, 7424, 7736

Offset: 1

Amarnath Murthy, Feb 20 2003

nonn

Cf. A080430, A080431.

2 * A011185(n).

sumset := {6}: keepA := array(1..10000): for m from 1 to 10000 do keepA[m] := 0 od: keepA[2] := 2: keepA[4] := 4: for n from 6 to 10000 by 2 do mytest := 0: for j from 2 to n-2 by 2 do if keepA[j]>0 then if member(keepA[j]+n, sumset) then mytest := 1; break; fi: fi: od: if mytest=0 then keepA[n] := n; for j from 2 to n-2 by 2 do sumset := sumset union {keepA[j]+n} od: fi: od: for i from 2 to 10000 by 2 do if keepA[i]>0 then printf(`%d,`, keepA[i]) fi: od: # James Sellers, Feb 26 2003

More terms from James Sellers, Feb 26 2003

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.

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