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%I #30 Sep 08 2022 08:44:47
%S 2,89,179,53639,53849,61409,63419,66749,126839,127139,143609,167729,
%T 186149,206369,254279,268049,296099,340919,405269,422069,446609,
%U 539009,594449,607319,658349,671249,725009,775949,810539,810809,812849,819509
%N Primes that remain prime through 4 iterations of function f(x) = 2x + 1.
%C Primes p such that 2*p+1, 4*p+3, 8*p+7 and 16*p+15 are also primes. - _Vincenzo Librandi_, Aug 04 2010
%C For n > 1, a(n) == 29 (mod 30). One should use it in codes. - _Zak Seidov_, Jan 31 2013
%H Harvey P. Dale, <a href="/A023302/b023302.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Prime[Range[10^4*4]], PrimeQ[a1=2*#+1] && PrimeQ[a2=2*a1+1] && PrimeQ[a3=2*a2+1] && PrimeQ[a4=2*a3+1] &] (* _Vladimir Joseph Stephan Orlovsky_, May 01 2008 *)
%t Join[{2},Select[Range[29,820000,30],And@@PrimeQ[NestList[2#+1&,#,4]]&]] (* _Harvey P. Dale_, Apr 03 2013 *)
%o (Magma) [n: n in [1..1200000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(4*n+3) and IsPrime(8*n+7) and IsPrime(16*n+15)] // _Vincenzo Librandi_, Aug 04 2010
%o (PARI) is(n)=isprime(n) && isprime(2*n+1) && isprime(4*n+3) && isprime(8*n+7) && isprime(16*n+15) \\ _Charles R Greathouse IV_, Jul 01 2013
%Y Cf. A005384, A005385, A007700, A023272, A023330, A057331, A005602.
%K nonn
%O 1,1
%A _David W. Wilson_
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