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
Examples
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.
Extensions
Corrected and extended by Jacques ALARDET and Eric Angelini, Aug 12 2008
Derangement wording introduced by Danny Rorabaugh, Nov 26 2015
Comments