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

1,1

Links

Table of n, a(n) for n=1..73.

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

Adjacent sequences: A336618 A336619 A336620 * A336622 A336623 A336624

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Jul 27 2020

Status

approved