cp's OEIS Frontend

For smallest son primes of order n see A136027 (also definition). For son primes of order 1 see A023208. For son primes of order 2 see A023218. For son primes of order 3 see A023225. For son primes of order 4 see A023235. For son primes of order 5 see A136082. For son primes of order 6 see A136083. For son primes of order 7 see A136084. For son primes of order 8 see A136085. For son primes of order 9 see A136086. For son primes of order 10 see A136087. For son primes of order 11 see A136088. For son primes of order 12 see A136089. For son primes of order 13 see A136090.

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524.

Primes of the form 7p+6 where p is prime. - David Radcliffe, Nov 30 2015

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072.

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073.

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073. For father primes of order 5 see A136074.

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073. For father primes of order 5 see A136074. For father primes of order 6 see A136075.

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073. For father primes of order 5 see A136074. For father primes of order 6 see A136075. For father primes of order 7 see A136075.

For smallest father primes of order n see A136026 (also definition). For father primes of order 1 see A094524. For father primes of order 2 see A136071. For father primes of order 3 see A136072. For father primes of order 4 see A136073. For father primes of order 5 see A136074. For father primes of order 6 see A136075. For father primes of order 7 see A136076. For father primes of order 8 see A136077.

For smallest father primes of order n, see A136026 (also definition). For father primes of orders 1,2,...,9, see A094524, A136071, A136072, A136073, A136074, A136075, A136076, A136077, A136078, respectively.

From Bob Selcoe, Apr 25 2014: (Start)

In general, a father prime, p', of order k is of the form p'=2k+(2k+1)*p for some prime, p. In this sequence, k=10, and so each prime is of the form p'=20+21p where p ranges over {3,7,11,13,19,23,...}. Thus a father prime p' has order k when (p'-2k)/(2k+1) is prime.

Father primes (p') of order k will be of the form: p'(mod (4k+2))=4k+1, or p'=(4k+2)*j-1, j>=2. For this sequence: k=10, 4k+2=42; j={2,4,6,7,10,12,...}. So for example, j=7 generates a father prime because 42*7-1 = 293 AND (293-(2*10))/(2*10+1) = 13, since both 13 and 293 are prime. Note that not all j such that (4k+2)*j-1 is prime will produce a father prime. In this example, when j=11, 42*11-1=461 (prime); but (461-(2*10))/(2*10+1) = 21 (not prime). (End)