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Lexicographically earliest sequence of different terms starting with a(1) = 2 such that the n-th digit of the sequence, placed in front of a(n) and then concatenated, produces a composite number.
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%I #9 Feb 20 2019 15:08:01

%S 2,3,4,5,6,7,8,9,11,12,14,1,15,13,16,17,18,19,21,22,23,24,25,26,28,29,

%T 27,31,32,34,35,36,33,37,38,42,39,43,44,45,41,46,48,47,49,51,52,54,53,

%U 55,56,57,58,61,62,63,64,65,59,66,67,68,72,69,73,71,74,75,76,77,78,81,82,83,79,84,85,86,88,89,87,91,92,94,95,96

%N Lexicographically earliest sequence of different terms starting with a(1) = 2 such that the n-th digit of the sequence, placed in front of a(n) and then concatenated, produces a composite number.

%C No digit 0 is admitted in a(n) in order to avoid leading zeroes after the concatenation.

%H Jean-Marc Falcoz, <a href="/A324280/b324280.txt">Table of n, a(n) for n = 1..10009</a>

%e The 1st digit of the sequence (2) concatenated to the 1st term = 22 (composite);

%e The 2nd digit of the sequence (3) concatenated to the 2nd term = 33 (composite);

%e The 3rd digit of the sequence (4) concatenated to the 3rd term = 44 (composite);

%e The 4th digit of the sequence (5) concatenated to the 4th term = 55 (composite);

%e The 5th digit of the sequence (6) concatenated to the 5th term = 66 (composite);

%e The 6th digit of the sequence (7) concatenated to the 6th term = 77 (composite);

%e The 7th digit of the sequence (8) concatenated to the 7th term = 88 (composite);

%e The 8th digit of the sequence (9) concatenated to the 8th term = 99 (composite);

%e The 9th digit of the sequence (1) concatenated to the 9th term = 111 (composite);

%e The 10th digit of the sequence (1) concatenated to the 10th term = 112 (composite);

%e etc.

%Y Cf. A306311, A306321, A324279, A324281 and A324282 where the same idea is used.

%K base,nonn

%O 1,1

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 20 2019