A210686 Primes p = 1 mod 6 such that all three iterations p=(6p+1) give primes = 1 mod 6.

61, 6361, 10771, 11311, 17791, 19471, 20011, 24391, 25951, 30091, 35251, 41911, 45631, 47431, 58711, 67891, 72271, 74161, 86341, 89821, 91711, 93001, 95311, 103171, 109321, 124021, 124171, 132961, 149491, 153871, 155731, 156151, 176461, 179461, 197551, 213181, 217681

Offset

1,1

Comments

All terms are = 1 mod 30.

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

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

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

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

Prog

(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", ")))}
(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
(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

Crossrefs

Subsequence of A002476.

Sequence in context: A167736 A015288 A219113 * A103915 A090823 A093261

Adjacent sequences: A210683 A210684 A210685 * A210687 A210688 A210689

Keyword

nonn

Author

Zak Seidov, Mar 28 2012

Status

approved