Repeated Prime-Differences

[Leroy Quet]

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,...


Related sequences which may or may not be in the EIS already:

* sequence of primes (with the possibility of repetitions) p(k+1), p(k), 
p(k-1)
where p(k+1) -p(k) = p(k) - p(k-1).
3,5,7,47,53,59,...


* the above sequence with distinct primes only.
  3,5,7,47,53,59,...

* the sequence of k's (the order of the primes p(k)).
  3, 16,...

*  the sequence of {p(k+1) -p(k)}'s
   when p(k+1) - p(k) = p(k) -p(k-1).
   2, 6,...

thanks,
Leroy Quet