Same sequence except for first term

[Leroy Quet]

I wonder about when it is okay and when it is not a good idea to add a 
sequence to the OEIS which varies from another sequence by only 1 term 
(specifically, but not limited to, the first term of the sequences).


For example:
Yesterday I sent these 2 sequences (along with the a(1)=3 and a(1)=5 
cases):

%S A000001 2, 0, 1, 1, 3, 2, 5, 4
%N A000001 a(n) = number of terms among {a(1),a(2),a(3),...a(n-1)} which 
are coprime to n; a(1)=2.
%C A000001 A family of related sequences can be generated using different 
positive integers for a(1). (a(1)=1 is sequence A096216.)
%Y A000001 A096216
%O A000001 1
%K A000001 ,more,nonn,
%A A000001 Leroy Quet (qq-quet at mindspring.com), Aug 27 2004

%S A000001 4, 0, 1, 1, 3, 2, 5, 4
%N A000001 a(n) = number of terms among {a(1),a(2),a(3),...a(n-1)} which 
are coprime to n; a(1)=4.
%C A000001 A family of related sequences can be generated using different 
positive integers for a(1). (a(1)=1 is sequence A096216.)
%Y A000001 A096216
%O A000001 1
%K A000001 ,more,nonn,
%A A000001 Leroy Quet (qq-quet at mindspring.com), Aug 27 2004

Since 2 and 4 are both powers of 2, these 2 sequences are the same except 
for their initial terms.

Also, we can have sequences such as:
a(m+1) = sum{k=1 to m} a(k)*k, a(1) =2
(a(k): 2, 2, 6, 24, 120,...),

and b(m) = m!,

which are the same sequences except that a(1) does not equal b(1).


The problem with simply having one of pair of such sequences in the 
database, and perhaps including a comment that the other sequence is 
similar except for one term, is that if someone does a search on the OEIS 
for the sequence with the term not in the OEIS, and includes the 
differing term in the search, then the sequence will not come up.

Yet I cannot help but worry that including every variation of a sequence 
will waste valuable bandwidth and A-numbers.

thanks,
Leroy Quet