A023272 Primes that remain prime through 3 iterations of the function f(x) = 2*x + 1.

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

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Intersection of A007700 and A023231.

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

Programs

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

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 *)

PARI

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