A023242 Primes that remain prime through 2 iterations of function f(x) = 2x + 3.

2, 5, 7, 13, 43, 47, 67, 97, 113, 137, 167, 173, 197, 277, 307, 397, 463, 467, 557, 607, 617, 887, 1063, 1153, 1217, 1237, 1307, 1373, 1427, 1453, 1523, 1553, 1567, 1663, 1693, 2027, 2113, 2143, 2203, 2617, 2647, 2707, 2777, 2857, 2927, 3343, 3613, 3767

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• easy

Comments

Primes p such that 2*p + 3 and 4*p + 9 are also primes. - Vincenzo Librandi, Aug 04 2010

All terms > 5 end in 3 or 7. - Robert Israel, Jun 22 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..7000

Programs

Magma

[p: p in PrimesUpTo(10000) | IsPrime(2*p+3) and IsPrime(4*p+9)] // Vincenzo Librandi, Aug 04 2010 (simplified by Bruno Berselli)

Maple

select(t -> isprime(t) and isprime(2*t+3) and isprime(4*t+9), [2,seq(2*i+1, i=1..10000)]); # Robert Israel, Jun 22 2015

Mathematica

Select[Range[4 10^6], PrimeQ[#]&& PrimeQ[2 # + 3]&&PrimeQ[4 # + 9] &] (* Vincenzo Librandi, Jun 24 2014 *)

PARI

is(n)=isprime(n) && isprime(2*n+3) && isprime(4*n+9) \\ Charles R Greathouse IV, Sep 09 2014

Sage

# By the definition:
def t(i): return 2*i+3
[p for p in primes(5000) if is_prime(t(p)) and is_prime(t(t(p)))] # Bruno Berselli, Sep 09 2014