A026443 a(n) = least positive integer > a(n-1) and not a(i)*a(j)+2 for 1<=i

1, 2, 3, 6, 7, 10, 11, 15, 18, 19, 25, 26, 29, 30, 33, 34, 37, 41, 42, 45, 46, 49, 50, 53, 57, 58, 61, 64, 65, 69, 73, 74, 78, 81, 82, 85, 88, 91, 95, 96, 99, 103, 106, 109, 114, 115, 119, 120, 123, 126, 127, 131, 134, 138, 139, 142, 143

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Similar sequences with different starting conditions: A026444 (1,3), A026445 (2,3), A026446 (2,4), A026447 (3,4).

Related sequences with definition using any products (not necessarily distinct) and with various starting conditions: A026448 (1,2), A026449 (1,3), A026450 (2,3), A026451 (2,4), A026452 (3,4).

Programs

Mathematica

a = {1, 2}; used = {a[[1]]*a[[2]] + 2}; Do[k = a[[-1]] + 1;
 While[MemberQ[used, k], k++]; used = Union[used, k*a + 2];
AppendTo[a, k], {n, 3, 60}]; a (* Ivan Neretin, Mar 06 2016 *)

Extensions

Name clarified by Robert C. Lyons, Feb 07 2025