A173701 Let S be the sequence and let D denote the sequence obtained by moving every third term three steps to the left. The D is the sequence of absolute values of the first differences of S.

1, 3, 2, 5, 9, 4, 13, 19, 6, 25, 32, 7, 39, 47, 8, 55, 65, 10, 75, 86, 11, 97, 109, 12, 121, 135, 14, 149, 164, 15

Offset

1,2

Comments

We also require that S be a permutation of the natural numbers and the lexicographically earliest sequence with the stated propoerty.

Links

Table of n, a(n) for n=1..30.

Eric Angelini, Hilbert Hotel and 3k rooms

E. Angelini, Hilbert Hotel and 3k rooms [Cached copy, with permission]

Example

Here is S:
S = ...1,3,2,5,9,4,13,19,6,25,32,7,39,47,8,55,65,10,75,86,11,97,109,12,121
The terms 2,4,6,7, ... move 3 places left.
After the moves we have:
D = .2,1,3,4,5,9,6,13,19,7,25,32,8,39,47,10,55,65,11,75,86,12,97,109,14,121
and D indeed gives the absolute values of the first differences of S.

Crossrefs

Sequence in context: A169755 A169748 A280875 * A116627 A254331 A210742

Adjacent sequences: A173698 A173699 A173700 * A173702 A173703 A173704

Keyword

nonn,more

Author

Eric Angelini, Nov 25 2010

Status

approved