Composites between primes

[Eric Angelini]

Hello SeqFan,
is this of interest?

2,4,6,7,8,9,10,12,13,14,15,16,18,20,21,23,24,25,26,27,28,30,32,37...
P ^ ^ P ^ ^ ^  ^  P.  ^  ^  ^  ^ ^  ^  P. ^  ^  ^  ^  ^  ^  ^  P.
   2       4                 6                    7   ...

Self-describing sequence : A(n) indicates the quantity
of composite numbers which are between two successive
primes.
(this is not an accurate definition -- please help me to
rephrase!)

If this is of interest, could someone compute more terms?

best,
É.