duplicate hunting, pt. 12

[Andrew Plewe]

On 5/8/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> Possible duplicates:
>
> A108639 and A109975
> http://www.research.att.com/~njas/sequences/?q=id:A108639|id:A109975

The definitions are identical.

> A080710 and A115837 (offsets are different)
> http://www.research.att.com/~njas/sequences/?q=id:A080710|id:A115837

Wow, it's cool if these are the same -- sure looks like they are!  But
I haven't written a proof.

> A038342 and A122596
> http://www.research.att.com/~njas/sequences/?q=id:A038342|id:A122596

The recursion given in the first sequence matches the GF of the
second, so once the first few terms are the same, they are the same
forever.

> A037314 and A037457
> http://www.research.att.com/~njas/sequences/?q=id:A037314|id:A037457

Yup, they are clearly identical.  The first one says in its formula
"numbers that can be written using only digits 0, 1, 2 in base 9" and
the other's definition says "write n in base 3, then treat it as a
base 9 number", hence getting all the numbers whose digits in base 9
are only 0, 1, 2.

> I think the title of A098037 doesn't accurately describe the sequence shown;
> "Number of divisors with multiplicity of the sums of two consecutive
> primes." I read "Number of divisors" to mean including non-prime as well as
> prime divisors. For the example shown in the sequence definition, A098037(2)
> = prime(2) + prime(3) = 3 + 5 = 8 = 2*2*2. Based on the title I believe 4
> and 8 (and maybe 1?) should also be included, so A098037(2) >= 5 (not sure
> if "with multiplicity" means that you'd also count another 2, as 4*2 = 8).
> As it stands, A105049 is a duplicate of this sequence. Perhaps the title of
> A098037 could be changed to "Number of prime divisors, counted with
> multiplicity, of the sum of two consecutive primes". Here is a link for
> comparison:
>
> http://www.research.att.com/~njas/sequences/?q=id:A098037|id:A105049

Yup, I think you are right -- they are the same sequence if you
understand "divisors with multiplicity" to mean "prime divisors with
multiplicity".

--Joshua Zucker



Straightforward duplicates:

A083907 and A084343
A048140 and A048238
A077220 and A125629 (after adjustment for offset in A125629)
A061504 and A119383
A064402 and A120743
A100597 and A100598
A087559 and A111297
A097577 and A097692
A081940 and A082270


Possible duplicates:

A026737 and A111279
http://www.research.att.com/~njas/sequences/?q=id:A026737|id:A111279

A116443 and A116444
http://www.research.att.com/~njas/sequences/?q=id:A116443|id:A116444

A054386 and A127450
http://www.research.att.com/~njas/sequences/?q=id:A054386|id:A127450

A061925 and A100796
http://www.research.att.com/~njas/sequences/?q=id:A061925|id:A100796


I've been skipping over submitting duplicate sequences like this pair:

http://www.research.att.com/~njas/sequences/?q=id:A026170|id:A026174

I assume that with their low A-numbers they've probably been reviewed and
are different. If that's not the case, then a search by the author's name
for sequences below A030000 should show all of them. I don't know how many
there are, but I've run into seven or eight pairs already.

Also, just a couple of observations about duplicates in the database
generally. I think it's a good idea for frequent contributers to do a search
for by author on their name and see if their sequences happen to appear
twice (usually with similar A numbers). Also, I think it'd be a good idea
for contributors to double-check their sequences after they're added by
clicking on those immediately proceeding and following in the "Sequence in
context" line. My rough estimate is that these two measures would decrease
duplicates by 80 or 90 percent.