A097481 Write the positive even integers on labels in numerical order, forming an infinite sequence L. Consider the succession of digits of L: 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8 3 0 ... (A036211). This sequence gives 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.

24, 6, 8, 10, 12, 14, 16, 18, 20, 2, 224, 26, 28, 30, 32, 34, 36, 38, 40, 4, 244, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132

Offset

1,1

Comments

Derangement here means the n-th element of L is not the n-th element of this sequence, so a(n) != 2n.

Links

Table of n, a(n) for n=1..65.

Example

We must begin with 2,4,6,8,... and we cannot have a(1) = 2, so the first possibility is the label "24". The next term must be the smallest available label not leading to a contradiction, thus "6". The next one will be "8", etc. After the label "20" the smallest available label is "2". After this "2" we cannot have a(11) = 22 -- we thus take the smallest available label which is "224". No label is allowed to start with a leading zero.

Crossrefs

Cf. A005843, A097484.

Sequence in context: A215752 A111803 A091737 * A267744 A040559 A339007

Adjacent sequences: A097478 A097479 A097480 * A097482 A097483 A097484

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