# 185 is special

Ralf Stephan ralf at ark.in-berlin.de
Fri Jun 1 17:38:20 CEST 2007

```You wrote
> 185 is the smallest positive number that doesn't start any sequence. Do you know anything special about 185 that might start a sequence?

There is nothing special about 185, as well as there is
nothing special about 10, even if it's base to our digital system.

ralf

I am wondering if this sequence is in the EIS. If it isn't, could someone

a(n) = the number of permutations {b(k)} of {1,2,3,...n} where b(m) does
not equal c(m) for all m, 1 <=m <=n, where {c(k)} is the inverse
permutation of {b(k)}.

For example, with the particular permutation of the first 4 positive
integers, (2,4,1,3), we have the inverse permutation (3,1,4,2). Since 2
doesn't = 3, 4 doesn't = 1, 1 doesn't = 4, and 3 doesn't = 2, this
permutation and its inverse are counted.

Obviously, every acceptable permutation is a derangement, but not the
other way around.

For example, the permutation (4,3,2,1) is a derangement, but its inverse
is also (4,3,2,1).

I get that the sequence {a(k)} begins: 0,0,2,6

I did a search for "0,2,6 permutations inverse" on the OEIS, and nothing
came up.

Could someone please calculate {a(k)}, and submit it if it isn't already
in the database?

Thanks,
Leroy Quet

```