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Lexicographically earliest sequence of different terms starting with a(1) = 10 such that the n-th digit of the sequence, placed after a(n) and then concatenated, produces a term with a parity opposed to the parity of a(n).
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%I #12 Jan 06 2020 12:19:02

%S 10,1,2,3,4,5,6,7,8,9,12,14,11,16,13,18,20,22,15,24,26,28,17,19,21,23,

%T 25,30,32,27,29,31,33,35,37,34,36,38,40,39,42,41,44,43,46,48,45,50,47,

%U 49,52,51,54,56,58,60,62,64,66,68,70,72,53,74,55,76,57,59,61,78,80,63,65,67,82,69,71,73,84,75,77,79,81,83,86

%N Lexicographically earliest sequence of different terms starting with a(1) = 10 such that the n-th digit of the sequence, placed after a(n) and then concatenated, produces a term with a parity opposed to the parity of a(n).

%C The sequence is a permutation of the numbers > 0.

%H Jean-Marc Falcoz, <a href="/A324282/b324282.txt">Table of n, a(n) for n = 1..10001</a>

%e The 1st digit of the sequence (1) concatenated to the 1st term = 101 (10 -> 101);

%e the 2nd digit of the sequence (0) concatenated to the 2nd term = 10 (1 -> 10);

%e the 3rd digit of the sequence (1) concatenated to the 3rd term = 21 (2 -> 21);

%e the 4th digit of the sequence (2) concatenated to the 4th term = 32 (3 -> 32);

%e the 5th digit of the sequence (3) concatenated to the 5th term = 43 (4 -> 43);

%e the 6th digit of the sequence (4) concatenated to the 6th term = 54 (5 -> 54);

%e the 7th digit of the sequence (5) concatenated to the 7th term = 65 (6 -> 65);

%e the 8th digit of the sequence (6) concatenated to the 8th term = 76 (7 -> 76);

%e the 9th digit of the sequence (7) concatenated to the 9th term = 87 (8 -> 87);

%e the 10th digit of the sequence (8) concatenated to the 10th term = 98 (9 -> 98);

%e the 11th digit of the sequence (9) concatenated to the 11th term = 129 (12 -> 129);

%e etc.

%Y Cf. A306311, A306321, A324279, A324280 and A324281 where the same idea is used.

%K base,nonn

%O 1,1

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