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A023272 Numbers n such that n remains prime through 3 iterations of function f(x) = 2x + 1. 34
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n, 2*n+1, 4*n+3 and 8*n+7 are primes. - Vincenzo Librandi, Aug 04 2010

At n > 2, a(n) == 29 mod 30. - Zak Seidov, Jan 31 2013

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

MAPLE

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

MATHEMATICA

Select[Prime[Range[10^3*4]], PrimeQ[a1=2*#+1] && PrimeQ[a2=2*a1+1] && PrimeQ[a3=2*a2+1] &] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)

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 *)

PROG

(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

(PARI) is(n)=isprime(n)&&isprime(2*n+1)&&isprime(4*n+3)&&isprime(8*n+7) \\ Charles R Greathouse IV, Mar 21 2013

CROSSREFS

Intersection of A007700 and A023231.

Cf. A005384, A005385, A023302, A023330, A057331, A005602.

Sequence in context: A120798 A048187 A082431 * A057978 A093308 A319230

Adjacent sequences:  A023269 A023270 A023271 * A023273 A023274 A023275

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)