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A097484
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Write the odd positive integers on labels in numerical order, forming an infinite sequence L. Consider the succession of single digits of L: 1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 ... (A031312). This sequence is a derangement of L that produces the same succession of digits, subject to the constraint that the smallest unused label must be used that does not lead to a contradiction.
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1
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13, 5, 7, 9, 1, 113, 15, 17, 19, 21, 23, 25, 27, 29, 3, 133, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 11, 1113, 115, 117, 119, 121, 123, 125, 127, 129, 131
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OFFSET
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1,1
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COMMENTS
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Derangement here means the n-th element of L is not the n-th element of this sequence, so a(n) != 2n - 1.
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LINKS
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EXAMPLE
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We must begin with 1,3,5,7... and we cannot have a(1) = 1, so the next possibility is the label "13". The next term must be the smallest available label not leading to a contradiction, thus "5". The next one will be "7", etc. After the label "9" the smallest available label is "1". After this "1" we cannot have a(6) = 11 -- we thus take the smallest available label which is "113". No label is allowed to start with a leading zero.
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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