increasing or decreasing subsequence

[bouyao]

Dear Henry,

its right that a(9)=30 (its my fault) but a(10)=51   and is different to
A000041
sequence A000041 is 1,1,2,3,5,7,11,15,22,30,42
but my sequence is 1,2,3,5,7,11,15,22,30,51

for a(10) we have 51 increasing subsequent
1,2,3,4,5,6,7,8,9,10
1,2,3,4,5,6,7,8,910
1,2,3,4,5,6,7,8910
1,2,3,4,5,6,78,910
1,2,3,4,5,6,78910
1,2,3,4,5,67,8910
1,2,3,4,5,678,910
1,2,3,4,5,678910
1,2,3,4,56,78,910
1,2,3,4,56,78910
1,2,3,4,567,8910
1,2,3,4,5678910
1,2,3,45,67,8910
1,2,3,45,678,910
1,2,3,45,678910
1,2,3,456,78910
1,2,3,4567,8910
1,2,3,45678910
1,2,34,56,78,910
1,2,34,56,78910
1,2,34,567,8910
1,2,34,5678910
1,2,345,678,910
1,2,345,678910
1,2,3456,78910
1,2,345678910
1,23,45,67,8910
1,23,45,678,910
1,23,45,678910
1,23,456,78910
1,23,4567,8910
1,23,45678910
1,234,567,8910
1,234,5678910
1,2345,678910
1,23456,78910
1,2345678910
12,34,56,78,910
12,34,56,78910
12,34,567,8910
12,34,5678910
12,345,678,910
12,345,678910
12,3456,78910
12,345678910
123,456,78910
123,4567,8910
123,45678910
1234,5678910
12345,678910
12345678910

thank you very much for your correction






----- Original Message ----- 
From: "Henry in Rotherhithe" <se16 at btinternet.com>
To: "bouyao" <bouyao at wanadoo.fr>; <seqfan at ext.jussieu.fr>
Sent: Saturday, March 13, 2004 10:42 PM
Subject: RE: increasing or decreasing subsequence


> I would have expected the initial sequence to be the same as the partition
> numbers http://www.research.att.com/projects/OEIS?Anum=A000041
> at least up to a(9)=30 rather than the 51 you have below.
>
> Indeed the only reason the sequences are not always the partition numbers
is
> that your concatentation is in decimal - a larger base would mean that we
> concatenated more single digits.
>
> Regards
>
> Henry Bottomley
>