[seqfan] Re: Decreasing runs - a permutation of the naturals
David Scambler
dscambler at bmm.com
Mon Aug 23 04:34:41 CEST 2010
> 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.
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