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A097488
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.
2
36, 9, 12, 15, 18, 21, 24, 27, 30, 3, 336, 39, 42, 45, 48, 51, 54, 57, 60, 6, 36, 669, 72, 75, 79, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165
OFFSET
1,1
COMMENTS
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.
Derangement here means the n-th element of L is not the n-th element of this sequence, so a(n) != 3n.
EXAMPLE
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
CROSSREFS
Cf. A008585.
Cf. A097481 for this sequence with multiples of 2.
Sequence in context: A181759 A280679 A343921 * A061046 A109256 A277983
KEYWORD
base,easy,nonn
AUTHOR
Eric Angelini, Sep 19 2004
EXTENSIONS
Corrected and extended by Jacques ALARDET and Eric Angelini, Aug 12 2008
Derangement wording introduced by Danny Rorabaugh, Nov 26 2015
STATUS
approved