# [seqfan] Re: Primitive composite terms of sequence

Fri Mar 2 16:04:04 CET 2012

```Dear seqfans,
Sorry, but my exaples in the previous message illustrate another definition of primitive composite terms which is, in my opinion, not less interesting. Therefore, I repeat my message in the following form:
"Let us call a composite term of INCREASING sequence {a(n)} primitive, if it is a product of  primes which are not in the sequence.  I believe that sequences of primitive composite 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,

----- Original Message -----
From: Vladimir Shevelev <shevelev at bgu.ac.il>
Date: Friday, March 2, 2012 16:06
Subject: [seqfan] Primitive composite terms of sequence
To: seqfan at list.seqfan.eu

> 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,
>