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%I #21 Nov 27 2015 10:13:08
%S 36,9,12,15,18,21,24,27,30,3,336,39,42,45,48,51,54,57,60,6,36,669,72,
%T 75,79,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,129,
%U 132,135,138,141,144,147,150,153,156,159,162,165
%N Write the positive multiples of 3 on labels in numerical order, forming an infinite sequence L. Now consider the succession of single digits of L: 3 6 9 1 2 1 5 1 8 2 1 2 4 2 7 3 0 3 3 3 6 3 9 4 2 .... 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 This could be roughly rephrased like this: Rewrite in the most economical way the "multiples-of-3 pattern" using only multiples of 3, but rearranged. No term in the sequence can appear more than once.
%C Derangement here means the n-th element of L is not the n-th element of this sequence, so a(n) != 3n.
%e We must begin with 3,6,9,12,... and we cannot have a(1) = 3, so the first possibility is the label "36". The next term must be the smallest available label not leading to a contradiction, thus "9". The next one will be "12", etc. After the label "30" the smallest available label is "3". After this "3" we cannot have a(11) = 33 -- we thus take the smallest available label which is "336". No label is allowed to start with a leading zero. - _Eric Angelini_, Aug 12 2008
%Y Cf. A008585.
%Y Cf. A097481 for this sequence with multiples of 2.
%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