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A125821
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Numbers n for which 8n+5 and 8n+7 are twin primes.
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7
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3, 12, 18, 24, 33, 57, 102, 132, 153, 159, 162, 234, 243, 249, 267, 279, 288, 297, 318, 348, 423, 432, 444, 447, 477, 489, 519, 528, 552, 564, 579, 627, 684, 687, 717, 774, 783, 837, 858, 918, 948, 969, 984, 993
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OFFSET
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1,1
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COMMENTS
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Proof that all numbers in this sequence are divisible by 3 (Zak Seidov Apr 19 2008:
if n=(3k+1), then 8n+7=8(3k+1)+7=3(5+8 k) (composite)
if n=(3k+2), then 8n+5=8(3k+2)+5=3(7+8 k) (composite),
so if we require that both 8n+5 and 8n+7 are primes, then n=3k, hence all terms in A125821 are multiples of 3. QED.
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LINKS
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MATHEMATICA
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Do[If[PrimeQ[8n + 5] && PrimeQ[8n + 7], Print[n]], {n, 1, 1000}]
Select[Range[3, 6000, 3], AllTrue[8#+{5, 7}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 14 2018 *)
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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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