Curious relation: (Where A121561(n) = 1) == A093515

[Max Alekseyev]

First off, the numbers n such that A121561(n)=1 are exactly numbers of
the form n=p or n=p+1, where p is a prime number.

Correspondingly, the numbers n such that A121561(n)=2 are exactly
numbers of the form n=q+p or n=q+p+1, where p and q are prime numbers
such that there are no primes in the interval [q+1,n].

Therefore, if Bob's observation is true, it implies a simpler
description for A093513 and A093515.
But I have not followed yet the definition of A093513 or A093515 to
justify that.

Regards,
Max

On Fri, Feb 29, 2008 at 1:04 PM, Ferenc Adorjan <fadorjan at freemail.hu> wrote:
>
>
>
> On Fri, Feb 29, 2008 at 6:27 PM, Robert G. Wilson v <rgwv at rgwv.com> wrote:
>
>
> >    But I have a bigger question. Is the sequence
> > "Where A121561(n) = 1" , A093515 "Transform of the prime sequence by the
> > Rule110 cellular automaton" and
> > "Where A121561(n) = 2" , A093513 "Transform of the prime sequence by the
> > Rule89 cellular automaton. ".
> >
> > Thanx, Bob.
> >
>
> It seems that Bob's observation is right, though it is very curious why...
> Does anybody has some idea?
>
> Ferenc
>