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Search: id:A125821
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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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+0
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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Proof that all numbers in this sequence are divisable 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 multriples of 3. QED.
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MATHEMATICA
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Do[If[PrimeQ[8n + 5] && PrimeQ[8n + 7], Print[n]], {n, 1, 1000}] (*Artur Jasinski*)
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CROSSREFS
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Cf. A001109.
Adjacent sequences: A125818 A125819 A125820 this_sequence A125822 A125823 A125824
Sequence in context: A047906 A104641 A032703 this_sequence A063229 A061564 A052637
For a(n)/3 see A139404.
Cf. A125822, A139402, A139404.
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KEYWORD
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nonn,new
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006
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