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A210686
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Primes p = 1 mod 6 such that all three iterations p=(6p+1) give primes = 1 mod 6.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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,...
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LINKS
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EXAMPLE
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a(1) = 61 because 6*61 + 1 = 367, 6*367 + 1 = 2203, and 6*2203 + 1 = 13219 are all primes = 1 mod 6.
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MATHEMATICA
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p=31; Reap[Do[If[Union[PrimeQ[NestList[6#+1&, p, 3]]]=={True}, Sow[p]]; p=p+30, {10^4}]][[2, 1]]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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