duplicate hunting cont.

Mitch Harris maharri at gmail.com
Tue Dec 11 01:53:06 CET 2007

```On Dec 10, 2007 5:17 PM, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> Possible duplicates:
> --------------------
>
> http://www.research.att.com/~njas/sequences/?q=id:A071683|id:A001076&fmt=1
> (aside from initial term in A001076)

They are identical except for the initial term and the 17. So they are
not exactly identical. But a comment could be added to A001076 to the
effect that they are averages of consecutive Fibonacci's (proof:
A001076 says it id F(3n)/2, averages of consecutive primes are
integers when they are both odd or (F(3n-2)+F(3n-1))/2 = F(3n)/2.

As to the conjecture in A071683...I wouldn't be surprised, but I'm not
about to try to prove it.

> http://www.research.att.com/~njas/sequences/?q=id:A041299|id:A001112&fmt=1
> (aside from initial zero in A001112)

If not for the reference, would be trivial.

Aside from that, the set of sequences of continued fractions of square
roots of nonsquares cries out for a systematic treatment (isn't there
a simple derivation of the recurrence at least? (except for common
divisors with the numerators))

> http://www.research.att.com/~njas/sequences/?q=id:A118579|id:A001297&fmt=1
> (aside from initial zero in A118579)

Yes, as stated in the comments of A001297.

> http://www.research.att.com/~njas/sequences/?q=id:A125121|id:A001481&fmt=1
> (duplicates as listed, will they ever differ?)
>
>
> Misc:
> ------
>
> http://www.research.att.com/~njas/sequences/?q=id:A087327|id:A000982&fmt=1
> (equation for A000982 already noted in comments to A087327, ought to have a
> reference to A000982)
>
> http://www.research.att.com/~njas/sequences/?q=id:A004729|id:A001317&fmt=1
> (A004729 is a subset of A001317)

One is finite the other not. The connection is commented on in both,
via A047999. But, yes, there should be a link directly between the
two.

--
Mitch

```