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.

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

Author

Eric Angelini, Sep 19 2004

Keywords

• base
• easy
• nonn

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.

Examples

			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.

Extensions

Corrected and extended by Jacques ALARDET and Eric Angelini, Aug 12 2008

Derangement wording introduced by Danny Rorabaugh, Nov 26 2015