Replace command

Hi ,

I have a sequence which looks like this

Lsat01000001
Lsat01000002
Lsat01000003
..
Lsat01000999
..
Lsat01100001
Lsat01278544

i want my output to look like this:

seq1
seq2
seq3
...
seq999
....
seq100001
....
seq278544

I used command but my output turned out as this:
sed 's/Lsat01/seq/g' filename >sortedfile

seq000001
seq000002
seq000003
...
seq000999
....

seq100001
....
seq278544

How can I get rid of additional zeroes

For example in seq 1, it shows as seq0000001 .

Please do advise.

s/Lsat010*/seq/