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%I #18 May 12 2022 15:17:54
%S 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,
%T 50,53,54,55,57,60,61,62,63,64,67,68,70,73,74,75,76,77,78,80,83,86,87,
%U 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
%N 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.
%e As a(1) = 2 and a(2) = 3, the product 2 * 3 = 6 cannot be in the sequence;
%e as a(2) = 3 and a(3) = 4, the product 3 * 4 = 12 cannot be in the sequence;
%e (...)
%e as a(6) = 8 and a(7) = 9, the product 8 * 9 = 72 cannot be in the sequence;
%e as a(8) = 10, the product 1 * 0 = 0 cannot be in the sequence;
%e as a(9) = 11, the product 1 * 1 = 1 cannot be in the sequence; etc.
%t 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 *)
%Y Cf. A203565.
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jul 27 2020
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