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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.
0
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
1,1
EXAMPLE
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.
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 *)
CROSSREFS
Cf. A203565.
Sequence in context: A357006 A137706 A324766 * A039224 A161508 A039264
KEYWORD
base,nonn
AUTHOR
STATUS
approved