Quote:
Originally Posted by sweety439
Is there a project of searching primes in these sequences?

have you read up on recursive relations and parity arguments etc before posting these because with that and modular arithmetic on polynomials under the polynomial remainder theorem I bet you could do a quick scan of them first yourself.
for example we know things like:
any polynomial without a certain number of odd coefficients including the constant term have certain properties like always being even or switching back and forth etc. just based on parity arguments we can say things like:
any polynomial with an even number of odd coefficients will pair those up under half the integer x values. any with an odd number of odd coefficients including the constant term will be odd at least half the time.
we know by the pigeonhole principle that given modular remainders only can be 0 to n1 ( n values) mod n that every n terms in a sequence has the same modular remainder mod n. etc.
for the relationship
we have the obvious statements like unless the two values you sum are opposite parity then the nth value will be even. since the only even prime is 2 it makes it hard to be prime and have this occur.