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A057620
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Initial prime in first sequence of n consecutive primes congruent to 1 modulo 6.
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9
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7, 31, 151, 1741, 1741, 1741, 19471, 118801, 148531, 148531, 406951, 2339041, 2339041, 51662593, 51662593, 73451737, 232301497, 450988159, 1444257673, 1444257673, 1444257673, 24061965043, 24061965043, 43553959717, 43553959717
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OFFSET
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1,1
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COMMENTS
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The sequence is infinite, by Shiu's theorem. - Jonathan Sondow, Jun 22 2017
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REFERENCES
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R. K. Guy, "Unsolved Problems in Number Theory", A4
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LINKS
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FORMULA
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EXAMPLE
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a(6) = 1741 because this number is the first in a sequence of 6 consecutive primes all of the form 3n + 1.
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MATHEMATICA
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p = 0; Do[a = Table[-1, {n}]; k = Max[1, p]; While[Union[a] != {1}, k = NextPrime[k]; a = Take[AppendTo[a, Mod[k, 3]], -n]]; p = NestList[NextPrime[#, -1] &, k, n]; Print[p[[-2]]]; p = p[[-1]], {n, 1, 18}] (* Robert G. Wilson v, updated by Michael De Vlieger, Sep 03 2016 *)
Table[k = 1; While[Total@ Boole@ Map[Mod[#, 6] == 1 &, NestList[NextPrime, Prime@ k, n - 1]] != n, k++]; Prime@ k, {n, 12}] (* Michael De Vlieger, Sep 03 2016 *)
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PROG
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(PARI) m=c=o=0; forprime(p=1, , p%6 != 1 && (!c||!c=0) && next; c||o=p; c++>m||next; m++; print1(", ", o)) \\ M. F. Hasler, Sep 03 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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