[seqfan] Primitive composite terms of sequence

[Vladimir Shevelev]

Recall that prime p is called primitive for sequence {a(n)}, if for some m, a(m) is multiple of p while none of a(i)  is  multiple of p for i<m. Let us call a composite term of {a(n)} primitive, if it is a product of NEW primitive primes. I believe that sequences of primitive composites terms of many sequences are of interest for OEIS. They arise, using the application of Eratosthenes-like algorithms for {a(n)}, therefore, they could be named also Eratosthenes pseudoprimes over {a(n)}. For example, the first two primitive composite terms for A002522 are 1157 and 1937; for A028387 they are 1891 and 2449, and I believe that there are infinitly many primitive composite terms for each of them.
Are similar sequences in OEIS? Other examples?
 
Regards,
Vladimir

 Shevelev Vladimir‎