A110095: non prime first differences

[Alec Mihailovs]

Alexandre Wajnberg wrote,

> This seq (this little handmade part!) seems to be reducible to 
> concatenated substrings
> a == 1 1 4 and
> b == 1 1 1 1 4 4 :
>
> (1 8 1 4) a a a b a a a b b a b...
>
> I wonder
> -if it's very the case (may be are there further other substrings of 1's 
> and 4's);
> -if there are super patterns in there, or possible regroupings of aaab's 
> and bab's?

It is easy to see that the positive integers that are not in A110095, are 
2,3,..., 8 and series of 3 consecutive numbers p, p+1, p+2 where p is a 
prime number such that p-2 is not prime (for every such p). Since there are 
sequences of consecutive non-prime numbers of length >=N-1, for example, 
N!+2,...N!+N for any N>1, the sequence of differences of  A110095 contains 
subsequences 1,1,...,1 of length >=N-1 for any N>1.

Alec Mihailovs
http://math.tntech.edu/alec/