A339582 - OEIS

%I #11 Dec 24 2020 21:11:08

%S 7,151,631,823,1063,1303,1783,2647,2887,3511,4423,4567,4951,5527,6007,

%T 6871,7351,7687,7927,8311,9127,10663,11383,11863,12007,12343,12487,

%U 13591,14071,15031,15607,15991,16087,17047,17191,17431,17623,17911,19207,20023,20407

%N Primes p = 8*r-1 such that all the prime factors of r are 7 mod 12.

%C Hugh Williams asks if this sequence is infinite.

%H Robert Israel, <a href="/A339582/b339582.txt">Table of n, a(n) for n = 1..10000</a>

%H R. K. Guy, editor, <a href="/A339579/a339579.pdf">Western Number Theory Problems, 1985-12-21 & 23</a>, Typescript, Jul 13 1986, Dept. of Math. and Stat., Univ. Calgary, 11 pages. Annotated scan of pages 1, 3, 7, 9, with permission. See Problem 85:16.

%p filter:= n ->

%p   isprime(n) and numtheory:-factorset((n+1)/8) mod 12 subset {7}:

%p select(filter, [seq(i,i=7..10^5,8)]); # _Robert Israel_, Dec 24 2020

%o (PARI) isok(p) = if (isprime(p) && (Mod(p, 8)== -1), my(r=(p+1)/8, f=factor(r)[,1]); #select(x->(Mod(x, 12) == 7), f) == #f); \\ _Michel Marcus_, Dec 24 2020

%Y Subsequence of A007522.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 24 2020

%E More terms from _Michel Marcus_, Dec 24 2020, who also added the initial term 7.