More conjectures?

[Antti Karttunen]

Antti Karttunen wrote:

> Ralf Stephan wrote:
>
> ...

...

>  Good work your list of hundred,
> when we will get the next one? .-)
>

One easy way to find interesting conjectures might be just
to search triplets Azzzzzz = Axxxxxx(Ayyyyyy(n)).
Now that many core and other important sequences have bfiles
this might be even practical. That is, as Axxxxxx one selects
a sequence with b-file, and as Ayyyyyy's one could use a small
set of common indexing sequences.
In addition to the the program should also check
indices Ayyyyyy(n)+1 and Ayyyyyy(n)-1),
e.g. for A000040 also A006093 and A008864
for A000045 also A000071 and A001611
maybe also for 2*Ayyyyyy(n), and partial sums, first differences, etc.

Of course one filters out those Azzzzzz which already have a reference 
to Axxxxxx.

Here are some of the indexing sequences from my hat that might
make good candidates for Ayyyyyy:

A005843 (even numbers) and with automatic +1, -1 also A005408 (odd numbers)
(similarly for other small multiples *3, *4, *5, ...)
A001651 (not divisible by 3)
A000040 (primes)
A001358 (semiprimes)
A002808 (composites)
A000045 (Fibonacci)
A000032 (Lucas)
A000201 (Lower Wythoff sequence (a Beatty sequence))
A001950 (Upper Wythoff sequence (a Beatty sequence))
A022342 (integers with "even" Zeckendorf-expansion)
A003622 (integers with "odd" Zeckendorf-expansion)
A000079 (2^n)
A000244 (3^n), etc.
A000108 (Catalans)
A014137 (their partial sums)
A000217 (triangular numbers, this finds the right edges of triangles, +1 
version the left edge)
A046092 (this finds the central diagonal of the triangles)
A000142 (n!)
A000290 (squares) (similarly, cubes, n^4)
A000037 (non-squares)
A005117 (square-free numbers)

...
and many other sequences from the list of the most cross-referenced ones.

Certain permutations could be also used:
e.g. A038722 finds transposes of triangles/arrays,
A056536 finds certain rarely used triangle readings, e.g. A028297.
Bit-fiddling permutations like A003188 (Gray code) could also find 
something interesting
in the land of bifurcative sequences. A059893, A054429, etc. might find 
alternative
readings for binary trees (like Stern-Brocot, etc.)


Terveisin,

Antti