twin primes (p,p+2)
A001359 Lesser of twin primes
3, 5, 11

cousin primes (p,p+4)
A046132 Larger member p+4 of cousin primes
7, 11, 17

3-tuples 

A022004 Initial members of prime triples (p,p+2,p+6)
5, 11, 17, 41