OFFSET
1,1
COMMENTS
If q, 18*q-1, 18*q+1 and 37*q+8 are prime, then 18*q-1 is in the sequence. Dickson's conjecture implies that there are infinitely many such q, and thus that this sequence is infinite.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3) = 107 is in the sequence because 107 and 109 are primes, A001414(108) = 2*2+3*3 = 13, and 107+13+109 = 229 is prime.
MAPLE
filter:= proc(p) isprime(p) and isprime(p+2) and isprime(2*p+2+add(s[1]*s[2], s=ifactors(p+1)[2])) end proc:select(filter, [seq(i, i=5..10^5, 6)]);
PROG
(PARI) \\ using A001414(n) written by M. F. Hasler
A001414(n)=(n=factor(n))[, 1]~*n[, 2];
forprime(p=3, 26000, my(pp1=p+1); if(isprime(p+2), if(isprime(A001414(pp1)+2*pp1), print1(p, ", ")))) \\ Hugo Pfoertner, Dec 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Dec 16 2019
STATUS
approved