Formerly Composite Numbers Sequence Definition

Construct a sequence of positive integers a(n) as follows: 


a(0) = 4
Each term a(n), other than the first, is the smallest number that satisfies the following:
a) a(n) is a composite number,
b) a(n) &gt; a(n-1), and
c) a(n) + a(k) + 1 is a composite number for each 0 &lt;= k &lt; n.


So we start with a(0) = 4. The next entry, a(1) must be 9. It can't be 5 or 7 since those aren't composite, and it can't be 6 or 8 because 6+4+1=11 is not composite and 8+4+1=13 is not composite. Finally, 9+4+1=14, which is composite, so a(1) = 9.

The next entry, a(2) must be 10, since it's the smallest number larger than 9 with 10+9+1=20 and 10+4+1=15 both composite.

For the next entry, 11 and 13 are both out because they're not composite. 12 is out because 12+4+1=17 which is not composite. 14 is out because 14+4+1=19 which is not composite. Thus, 15 is the next term of the sequence because 15 is composite and 15+4+1=20, 15+9+1=25, and 15+10+1=26 are all each composite, so a(3) = 15.

Here are the first 30 terms in this sequence:

4, 9, 10, 15, 16, 22, 28, 34, 35, 39, 40, 46, 52, 58, 64, 70, 75, 76, 82, 88, 94, 100, 106, 112, 118, 119, 124, 125, 130, 136


This is OEIS A133764.

Challenge

Given an input integer n, output the nth term in this sequence.

Rules


You can choose either 0- or 1-based indexing. Please state which in your submission.
The input and output can be assumed to fit in your language's native integer type.
The input and output can be given by any convenient method.
Either a full program or a function are acceptable. If a function, you can return the output rather than printing it.
Standard loopholes are forbidden.
This is code-golf so all usual golfing rules apply, and the shortest code (in bytes) wins.
Husk, 11 bytes

!üȯṗ→+fotpN


1-indexed.
Try it online!

Explanation

!üȯṗ→+fotpN  Implicit input, a number n.
          N  The list of positive integers [1,2,3,4,..
      f      Keep those
         p   whose list of prime factors
       ot    has a nonempty tail: [4,6,8,9,10,12,..
 ü           De-duplicate wrt this equality predicate:
     +       sum
    →        plus 1
  ȯṗ         is a prime number.
             Result is [4,9,10,15,16,..
!            Get n'th element.