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A023272
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Primes that remain prime through 3 iterations of the function f(x) = 2*x + 1.
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35
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2, 5, 89, 179, 359, 509, 1229, 1409, 2699, 3539, 6449, 10589, 11549, 11909, 12119, 17159, 19709, 19889, 22349, 26189, 27479, 30389, 43649, 53639, 53849, 55229, 57839, 60149, 61409, 63419, 66749, 71399, 74699, 75329, 82499, 87539, 98369, 101399, 104369
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OFFSET
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1,1
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COMMENTS
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Primes p such that 2*p+1, 4*p+3 and 8*p+7 are also primes. - Vincenzo Librandi, Aug 04 2010
For n > 2, a(n) == 29 (mod 30). - Zak Seidov, Jan 31 2013
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LINKS
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MAPLE
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p:=2: for n from 1 to 5000 do if(isprime(2*p+1) and isprime(4*p+3) and isprime(8*p+7))then printf("%d, ", p): fi: p:=nextprime(p): od: # Nathaniel Johnston, Jun 30 2011
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MATHEMATICA
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Join[{2, 5}, Select[Range[89, 104369, 30], PrimeQ[#] && PrimeQ[2*# + 1] && PrimeQ[4*# + 3] && PrimeQ[8*# + 7] &]] (* Zak Seidov, Jan 31 2013 *)
p3iQ[n_]:=AllTrue[NestList[2#+1&, n, 3], PrimeQ]; Join[{2, 5}, Select[ Range[ 89, 200000, 30], p3iQ]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 30 2019 *)
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PROG
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(Magma) [n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(4*n+3) and IsPrime(8*n+7)] // Vincenzo Librandi, Aug 04 2010
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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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