OFFSET
0,3
COMMENTS
Conjecture: Number of permutations sigma such that (sigma(k) mod sigma(k+1)) < (sigma(k+1) mod sigma(k+2)) for 1 <= k <= n - 2 is equal to A022825(n). This is true for n <= 19.
EXAMPLE
b(n) = sigma(n) mod sigma(n+1).
In case of n = 3.
| | b(1),b(2)
----+-----------+----------
1 | [1, 2, 3] | [1, 2] *
2 | [1, 3, 2] | [1, 1]
3 | [2, 1, 3] | [0, 1] *
4 | [3, 1, 2] | [0, 1] *
In case of n = 4.
| | b(1),b(2),b(3)
----+--------------+---------------
1 | [1, 2, 3, 4] | [1, 2, 3] *
2 | [1, 3, 2, 4] | [1, 1, 2]
3 | [1, 4, 3, 2] | [1, 1, 1]
4 | [2, 1, 3, 4] | [0, 1, 3] *
5 | [2, 1, 4, 3] | [0, 1, 1]
6 | [3, 1, 2, 4] | [0, 1, 2] *
7 | [4, 1, 2, 3] | [0, 1, 2] *
8 | [4, 1, 3, 2] | [0, 1, 1]
9 | [4, 2, 1, 3] | [0, 0, 1]
* (strongly increasing)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 27 2020
EXTENSIONS
a(17)-a(20) from Alois P. Heinz, Feb 27 2020
a(21)-a(22) from Giovanni Resta, Mar 03 2020
a(23)-a(31) from Bert Dobbelaere, Mar 12 2020
a(32) from Bert Dobbelaere, Mar 15 2020
STATUS
approved