[seqfan] Re: Gilbreath mysteries

[Thomas Scheuerle]

I think I found partly an answer onto my last questions.
There needs to be an upper bound on all rows to obtain
a first column full of ones.
In the process of sieving the primes, the set of possible future candidates
gets which each new obtained prime more complicated in its structure.
A more "complicated" and more "unordered" sequence has slower decaying
absolute differences of higher order so it seems naturally
that for each row in the GT array an upper limit which does on the prime index will exist. 
I conjecture that a sequence which such limits growing slow enough
for all rows may then exhibit such a first column of ones.



> Regarding question 2, let us replace the primes with something else:
> 2,3,7,13,21,31,43     2, A002061
> 1,2,4,6,8,10,12
> 1,2,2,2,2,2 ,2,
> 1,0,0,0,0,0,0
> 1,0,0,0,0,0,0
> 1,0,0,0,0,0
> 
> If we have a slower growing sequence of odd numbers in the first row,
> will we still see all ones in the first column ? 
> What kind of sequences could be the exceptions ?
>