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A090839
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Numbers n such that 6*n+1, 6*n+7, 6*n+13, 6*n+19 are consecutive primes.
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11
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290, 550, 850, 1060, 2650, 3035, 3245, 5015, 5105, 8935, 10615, 11890, 12925, 13485, 13905, 14850, 15215, 15985, 17560, 17600, 18105, 19925, 20135, 21780, 23510, 24040, 25490, 28830, 31145, 34365, 36355, 38140, 38370, 42025, 43845, 46820, 47575, 48745, 49130, 50495, 53350
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OFFSET
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1,1
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COMMENTS
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All terms are == 0 (mod 5). - Robert G. Wilson v, Dec 12 2017
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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6*290 + 1 = 1741, 6*290 + 7 = 1747, 6*290 + 13 = 1753, 6*290 + 19 = 1759 and 1741, 1747, 1753, 1759 are consecutive primes, so 290 is a term.
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MAPLE
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P:=proc(n) if isprime(6*n+1) and isprime(6*n+7) and isprime(6*n+13) and isprime(6*n+19) and not isprime(6*n+5) and not isprime(6*n+11) and not isprime(6*n+17) then n; fi; end: seq(P(i), i=1..10^5); # Paolo P. Lava, Dec 07 2017
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MATHEMATICA
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Block[{nn = 50500, s}, s = Select[Prime@ Range@ PrimePi[6 (nn + 3) - 1], Divisible[(# + 1), 6] &]; Select[Range@ nn, And[AllTrue[#, PrimeQ], Count[s, q_ /; First[#] < q < Last@ #] == 0] &@ Map[6 # + 1 &, # + Range[0, 3]] &]] (* Michael De Vlieger, Dec 06 2017 *)
fQ[n_] := Block[{p = {6n +1, 6n +7, 6n +13, 6n +19}}, Union@ PrimeQ@ p == {True} && NextPrime[6n +1, 3] == 6n +19]; Select[5 Range@ 10100, fQ] (* Robert G. Wilson v, Dec 12 2017 *)
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PROG
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(PARI) isok(n) = my(p, q, r); isprime(p=6*n+1) && ((q=6*n+7) == nextprime(p+1)) && ((r=6*n+13) == nextprime(q+1)) && (6*n+19 == nextprime(r+1)); \\ Michel Marcus, Sep 20 2019
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CROSSREFS
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Cf. A033451, A090832, A090833, A090834, A090835, A090836, A090837, A090838.
Sequence in context: A075421 A332229 A296055 * A158255 A295483 A075299
Adjacent sequences: A090836 A090837 A090838 * A090840 A090841 A090842
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Pierre CAMI, Dec 09 2003
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EXTENSIONS
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Missing term 5105 and more terms from Michel Marcus, Sep 20 2019
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STATUS
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approved
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