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A308232
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Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the concatenation kd, d being the digit that was read and k the number of d's present so far in the sequence.
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3
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1, 11, 21, 31, 12, 41, 13, 51, 61, 22, 14, 71, 81, 23, 15, 91, 16, 101, 32, 42, 111, 24, 17, 121, 18, 131, 52, 33, 141, 25, 19, 151, 161, 26, 171, 10, 181, 43, 62, 34, 72, 191, 201, 211, 82, 44, 221, 27, 231, 92, 241, 251, 28, 261, 53, 271, 35, 102, 63, 73, 281, 54, 291, 112, 45, 301, 29, 311, 55, 321, 331, 36, 341, 122, 46, 351
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OFFSET
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1,2
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COMMENTS
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All integers > 0 will appear exactly once, except 2, 3, 4, 5, 6, 7, 8 and 9 which will never appear.
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LINKS
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EXAMPLE
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The sequence starts with a(1) = 1.
We read this 1, see that there is only one digit 1 so far in the sequence, thus k = 1; we have then [kd] = 11 and this 11 becomes a(2);
We read now the first digit of a(2) = 11, which is 1; as this 1 is the 2nd occurrence of 1 so far in the sequence, we have k = 2 and [kd] = 21; this 21 becomes a(3);
We read now the second digit of a(2) = 11, which is 1; as this 1 is the 3rd occurrence of 1 so far in the sequence, we have k = 3 and [kd] = 31; this 31 becomes a(4);
We read now the first digit of a(3) = 21, which is 2; as this 2 is the 1st occurrence of 2 so far in the sequence, we have k = 1 and [kd] = 12; this 12 becomes a(5);
We read now the second digit of a(3) = 21, which is 1; as this 1 is the 4th occurrence of 1 so far in the sequence, we have k = 4 and [kd] = 41; this 41 becomes a(6); etc.
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CROSSREFS
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Cf. A325721 and A325722 where the same idea is developed (addition and multiplication instead of concatenation).
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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