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%I #15 Nov 26 2015 23:55:42
%S 13,5,7,9,1,113,15,17,19,21,23,25,27,29,3,133,35,37,39,41,43,45,47,49,
%T 51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,
%U 97,99,101,103,105,107,109,11,1113,115,117,119,121,123,125,127,129,131
%N 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.
%C Derangement here means the n-th element of L is not the n-th element of this sequence, so a(n) != 2n - 1.
%e 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.
%Y Cf. A005408, A097481, A097485, A097487, A097488, A097500, A097912, A097962, A098067, A098080.
%Y Same type of sequence -- but for even numbers -- is A097481. - _Eric Angelini_, Aug 12 2008
%K base,easy,nonn
%O 1,1
%A _Eric Angelini_, Sep 19 2004
%E Corrected and extended by _Jacques ALARDET_ and _Eric Angelini_, Aug 12 2008
%E Derangement wording introduced by _Danny Rorabaugh_, Nov 26 2015
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