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A057622
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Initial prime in first sequence of n consecutive primes congruent to 5 modulo 6.
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11
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5, 23, 47, 251, 1889, 7793, 43451, 243161, 726893, 759821, 1820111, 1820111, 10141499, 19725473, 19725473, 136209239, 400414121, 400414121, 489144599, 489144599, 766319189, 766319189, 21549657539, 21549657539, 21549657539, 140432294381, 140432294381, 437339303279, 1871100711071, 3258583681877
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OFFSET
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1,1
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COMMENTS
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Same as A057621 except for a(1). See A057620 for primes congruent to 1 (mod 6). See A055626 for the variant "exactly n", which is an upper bound, cf. formula. - M. F. Hasler, Sep 03 2016
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(12) = 1820111 because this number is the first in a sequence of 12 consecutive primes all of the form 6n + 5.
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MATHEMATICA
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p = 0; Do[a = Table[-1, {n}]; k = Max[1, p]; While[Union@ a != {5}, k = NextPrime@ k; a = Take[AppendTo[a, Mod[k, 6]], -n]]; p = NestList[NextPrime[#, -1] &, k, n]; Print[p[[-2]]]; p = p[[-1]], {n, 18}] (* Robert G. Wilson v, updated by Michael De Vlieger, Sep 03 2016 *)
Table[k = 1; While[Total@ Boole@ Map[Mod[#, 6] == 5 &, NestList[NextPrime, Prime@ k, n - 1]] != n, k++]; Prime@ k, {n, 12}] (* Michael De Vlieger, 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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Three lines of data (derived from J.K.Andersen's web page) completed by M. F. Hasler, Sep 02 2016
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STATUS
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approved
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