Possible new OEIS - sequence: prime-run lengths in A007310

[Stephen Steiner]

I am considering the sequence of lengths of maximal blocks of consecutive prime terms in A007310 (numbers congruent to 1 or 5 mod 6).

It begins

7,2,4,1,2,3,2,1,6,2,2,2,1,2,1,2,4,1,4,2,...

coming from the prime blocks

[5,7,11,13,17,19,23], [29,31], [37,41,43,47], [53], [59,61], [67,71,73], ...

Equivalently, if c(n)=A038509(n), then after the initial 7 this is the sequence of positive values of pi(c(n+1)) - pi(c(n)).

This is different from A348168, which segments the primes by a gap condition and begins

1,1,1,1,2,2,1,2,4,...

Does this look like a natural OEIS candidate, or is there already a closer existing entry?