[seqfan] Re: Decreasing runs - a permutation of the naturals

[David Scambler]

> Alex M 
> I wonder if there are an infinite of number of sequences like the two you
> have mentioned?

There are. The members chosen for a descending or ascending group are arbitrary. The only requirement is that the length of run n matches a(n) and that you eventually use every natural number once. Starting the sequence with a(1) = 2 is also arbitrary; any number > 1 will do. E.g. 3 2 1 | 5 4 | 6 | 11 10 9 8 7 | .... 

The sequence as originally given obeys the additional rule "each a(n) has the minimum possible value". As such it is unique.