A210686 - OEIS

%I #20 Mar 17 2023 07:12:34

%S 61,6361,10771,11311,17791,19471,20011,24391,25951,30091,35251,41911,

%T 45631,47431,58711,67891,72271,74161,86341,89821,91711,93001,95311,

%U 103171,109321,124021,124171,132961,149491,153871,155731,156151,176461,179461,197551,213181,217681

%N Primes p = 1 mod 6 such that all three iterations p=(6p+1) give primes = 1 mod 6.

%C All terms are = 1 mod 30.

%C Note that 4th iteration gives composite integer = 5 mod 10.

%C (a(n)-1)/30 = 2, 212, 359, 377, 593, 649, 667, 813, 865,...

%H Zak Seidov, <a href="/A210686/b210686.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 61 because 6*61 + 1 = 367, 6*367 + 1 = 2203, and 6*2203 + 1 = 13219 are all primes = 1 mod 6.

%t p=31;Reap[Do[If[Union[PrimeQ[NestList[6#+1&,p,3]]]=={True},Sow[p]];p=p+30,{10^4}]][[2,1]]

%o (PARI) {p=31; for(i=1,10^4,p=p+30; if(isprime(p)&&isprime(q=6*p+1)&&isprime(r=6*q+1)&&isprime(6*r+1),print1(p",")))}

%o (PARI) forprime(p=2,1e6,if(p%30<2&&isprime(6*p+1)&&isprime(36*p+7)&&isprime(216*p+43),print1(p", "))) \\ _Charles R Greathouse IV_, Mar 29 2012

%o (Magma) [p: p in PrimesUpTo(22*10^4) | p mod 6 eq 1 and forall{q: i in [1..3] | IsPrime(q) where q is (6^i*(5*p+1)-1) div 5}]; // _Bruno Berselli_, Mar 29 2012

%Y Subsequence of A002476.

%K nonn

%O 1,1

%A _Zak Seidov_, Mar 28 2012