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A180427 Lexicographically earliest permutation of the positive integers such that the inverse permutation is also the absolute value of the first differences. 1
1, 2, 4, 10, 13, 3, 19, 38, 16, 5, 9, 73, 48, 43, 23, 6, 15, 42, 7, 14, 45, 8, 49, 64, 12, 72, 17, 50, 97, 154, 20, 95, 27, 98, 18, 83, 21, 99, 91, 173, 22, 107, 89, 103, 190, 169, 28, 117, 104, 127, 155, 24, 118, 219, 26, 135, 29, 142, 258, 25, 147, 36, 181, 11, 35, 159 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

Let a(n) be this sequence and b(n)=|a(n)-a(n+1)| be the inverse permutation of this sequence.

After a(1)=1, a(2)=2, a(3)=4, the next term, a(4), cannot be a repeat of 1,2, or 4 since by definition a(n) must be a permutation of the positive integers.

It cannot be 3,5, or 6, as that would force b(3)=1 or 2 (a repeat of b(1)=1, or b(2)=2).

We cannot have a(4)=7, because b(3)=3 implies a(3)=3, which contradicts a(3)=4.

We cannot have a(4)=8, because b(3)=4 implies a(4)=3.

We cannot have a(4)=9, because b(3)=5 implies a(5)=3, and b(4)=|a(5)-a(4)|=6 which contradicts b(4)=3 as implied by a(3)=4.

Therefore a(4)=10 is the smallest value of a(4) which will not generate a contradiction.

CROSSREFS

Cf. A180428 - Inverse Permutation of this sequence. Also the first differences (absolute value) of this sequence.

Sequence in context: A181495 A092367 A216814 * A127591 A100912 A174721

Adjacent sequences:  A180424 A180425 A180426 * A180428 A180429 A180430

KEYWORD

nice,nonn

AUTHOR

Andrew Weimholt, Sep 04 2010

STATUS

approved

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Last modified October 23 12:42 EDT 2021. Contains 348214 sequences. (Running on oeis4.)