[seqfan] a permutation of the naturals

[Andrew Weimholt]

This idea was inspired by one of Eric Angelini's recent posts (angry numbers).

We start with the natural numbers in their normal positions,
and then the number in position 1 (which happens to be 1), catapults
the number to its right to a position 1 further to the right.
So after the first step, we have 1,3,2,4,5,6,7,8...
Then the number now in position 2, (which is 3), catapults the number
to its right (which is 2) to a position 3 further to the right
Now we have, 1,3,4,5,6,2,7,8...
In the nth step, the number now in the nth position (which will be
a(n)) catapults the number to its right to a position a(n) further to
the right.

The sequence, beginning at n=1 is...

1, 3, 4, 6, 7, 5, 10, 2, 13, 12, 14, 16, 18, 19, 21,
23, 8, 25, 15, 28, 17, 24, 32, 33, 20, 36, 22, 38, 40, 41, 42,
44, 45, 47, 31, 35, 50, 52, 27, 55, 11, 58, 59, 61, 63, 64, 66,

The inverse permutation is...

1, 8, 2, 3, 6, 4, 5, 17, 152, 7, 41, 10, 9, 11, 19,
12, 21, 13, 14, 25, 15, 27, 16, 22, 18, 57, 39, 20,

The following sequence gives the number of times n is catapulted

0, 3, 0, 0, 1, 0, 0, 2, 6, 0, 3, 1, 0, 0, 1,
0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 2, 2, 0,

Not sure these are worth submitting, but thought I'd at least share
them the seqfan list

Andrew