Repeated Prime-Differences

[Hugo Pfoertner]

Leroy Quet wrote:
> 
> It appears that the following sequence(s) is/are not in the EIS, somewhat
> surprisingly.
> (Could someone please compute them and submit. thanks.)
> 
> If p(k) is the k_th prime,
> 
> the sequence consists of primes p where
> 
> p(k+1) - p = p - p(k-1),
> 
> if k is such that p(k) = p.
> 
> I get: 5, 53,...
> 
[...]
> 
> thanks,
> Leroy Quet

If you are looking for records of differences to the next prime
neighbors, then the relevant sequences might be Harvey Dubner's
"Equidistant lonely primes" in
http://www.research.att.com/projects/OEIS?Anum=A058867
http://www.research.att.com/projects/OEIS?Anum=A058868
http://www.research.att.com/projects/OEIS?Anum=A058869

When looking at the definition of A058869, I found the sentence in the
Name field:
"The distances corresponding to the above sequence are
2,6,12,18,24...114,120,126,144."

Can someone tell me the reason for the omission of 132 and 138 between
126 and 144? I tried to re-compute A058869 using the definition "First
occurrence of an equidistant lonely prime that is surrounded by gaps 6*n
and didn't find matching primes <2^31 for the gaps 132 and 138. Can
someone try to find the corresponding terms of A058869? Otherwise the
final term 383204683 of A058869 should be removed.

Hugo Pfoertner