OFFSET
1,1
COMMENTS
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)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
n = 10; a = {}; Do[If[PrimeQ[(Prime[k] - 2n)/(2n + 1)], AppendTo[a, Prime[k]]], {k, 1, 1500}]; a
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Dec 12 2007
STATUS
approved