OFFSET
1,1
COMMENTS
This sequence arises from a more general study. First, consider a function f : P -> N (where P is the set of the odd prime numbers) such that 0 <= f(p) < p. Then, remove from the set P each prime number q such that q = f(p) (mod p) for some p.
For example, if f(p) = 0 for each p, then the final set is the empty set.
If f(p) = 1 for each p, then the final set seems to be the set of Fermat primes (empirical observation).
If f(p) = p-1, then the final set seems to be the set of Mersenne primes (empirical observation).
For the particular choice f(p) = 2k (where p is the k-th odd prime) this sequence is obtained.
LINKS
Mathematics StackExchange, Can the set of odd primes be finitely sieved by arbitrary congruences of primes?
EXAMPLE
Terms in this sequence are those odd primes that are neither congruent to 2 (mod 3), nor congruent to 4 (mod 5), nor congruent to 6 (mod 7), nor congruent to 8 (mod 11), etc.
7 is a term because 7 == 1 (mod 3) and 7 == 2 (mod 5).
11 is not a term because 11 == 2 (mod 3).
13 is not a term because 13 == 6 (mod 7).
17 is not a term because 17 == 2 (mod 3).
19 is not a term because 19 == 8 (mod 11).
PROG
(PARI) isok(p) = {if(!isprime(p)||p==2, 0, my(k=0); forprime(q=3, p-1, k+=2; if(p%q==k, return(0))); 1) } \\ Andrew Howroyd, Jan 11 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrea La Rosa, Jan 11 2023
EXTENSIONS
Terms a(15) and beyond from Andrew Howroyd, Jan 11 2023
STATUS
approved