A023302 Primes that remain prime through 4 iterations of function f(x) = 2x + 1.

2, 89, 179, 53639, 53849, 61409, 63419, 66749, 126839, 127139, 143609, 167729, 186149, 206369, 254279, 268049, 296099, 340919, 405269, 422069, 446609, 539009, 594449, 607319, 658349, 671249, 725009, 775949, 810539, 810809, 812849, 819509

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

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

For n > 1, a(n) == 29 (mod 30). One should use it in codes. - Zak Seidov, Jan 31 2013

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005384, A005385, A007700, A023272, A023330, A057331, A005602.

Programs

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

Mathematica

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 *)
Join[{2},Select[Range[29,820000,30],And@@PrimeQ[NestList[2#+1&,#,4]]&]] (* Harvey P. Dale, Apr 03 2013 *)

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