A180427 Lexicographically earliest permutation of the positive integers such that the inverse permutation is also the absolute value of the first differences.

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

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: A092367 A366773 A216814 * A127591 A100912 A174721

Adjacent sequences: A180424 A180425 A180426 * A180428 A180429 A180430

Keyword

nice,nonn

Author

Andrew Weimholt, Sep 04 2010

Status

approved