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A097484 Write the odd positive integers on labels in numerical order, forming an infinite sequence L. Consider the succession of single digits of L: 1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 ... (A031312). 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. 1
13, 5, 7, 9, 1, 113, 15, 17, 19, 21, 23, 25, 27, 29, 3, 133, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 11, 1113, 115, 117, 119, 121, 123, 125, 127, 129, 131 (list; graph; refs; listen; history; text; internal format)
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 - 1.

LINKS

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

EXAMPLE

We must begin with 1,3,5,7... and we cannot have a(1) = 1, so the next possibility is the label "13". The next term must be the smallest available label not leading to a contradiction, thus "5". The next one will be "7", etc. After the label "9" the smallest available label is "1". After this "1" we cannot have a(6) = 11 -- we thus take the smallest available label which is "113". No label is allowed to start with a leading zero.

CROSSREFS

Cf. A005408, A097481, A097485, A097487, A097488, A097500, A097912, A097962, A098067, A098080.

Same type of sequence -- but for even numbers -- is A097481. - Eric Angelini, Aug 12 2008

Sequence in context: A010218 A107833 A248146 * A098326 A302208 A068662

Adjacent sequences:  A097481 A097482 A097483 * A097485 A097486 A097487

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

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Last modified June 28 21:04 EDT 2022. Contains 354907 sequences. (Running on oeis4.)