A336621 Lexicographically earliest sequence of distinct positive terms starting with a(1) = 2 such that the product of the last two digits of the sequence (when extended with a new term) is not in the sequence.

2, 3, 4, 5, 7, 8, 9, 10, 11, 16, 23, 26, 27, 29, 30, 32, 34, 36, 37, 38, 40, 43, 45, 46, 47, 50, 53, 54, 55, 57, 60, 61, 62, 63, 64, 67, 68, 70, 73, 74, 75, 76, 77, 78, 80, 83, 86, 87, 89, 90, 92, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 116, 120, 123, 126, 127, 129, 130, 132

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Jul 27 2020

Keywords

• base
• nonn

Examples

			As a(1) = 2 and a(2) = 3, the product 2 * 3 = 6 cannot be in the sequence;
as a(2) = 3 and a(3) = 4, the product 3 * 4 = 12 cannot be in the sequence;
(...)
as a(6) = 8 and a(7) = 9, the product 8 * 9 = 72 cannot be in the sequence;
as a(8) = 10, the product 1 * 0 = 0 cannot be in the sequence;
as a(9) = 11, the product 1 * 1 = 1 cannot be in the sequence; etc.
		

Crossrefs

Cf. A203565.

Programs

Mathematica

lst={};a[1]=2;a[n_]:=a[n]=Block[{k=2},While[s=Array[a,n-1];AppendTo[lst,p=Times@@(Flatten[IntegerDigits/@Join[Last@s,{k}]][[-2;;]])];MemberQ[s,p]||MemberQ[s,k]||MemberQ[lst,k],k++;lst=Most@lst];k];Array[a,73] (* Giorgos Kalogeropoulos, May 12 2022 *)