A153645 - OEIS

%I #14 Sep 08 2022 08:45:40

%S 3,5,7,13,17,47,67,73,137,167,277,307,313,487,503,593,607,613,787,823,

%T 1117,1123,1237,1523,1543,1637,1987,2777,2887,3037,3163,3433,3457,

%U 3463,3797,3853,4093,4283,4583,5113,5297,5323,5683,5953,6047,6577,6803,6823

%N Primes p such that p^2 + 4 and p^2 + 4p + 2 are also prime.

%C Subsequence of A062324.

%H Vincenzo Librandi, <a href="/A153645/b153645.txt">Table of n, a(n) for n = 1..1000</a>

%e For prime p = 3, p^2+4 = 13 and p^2+4p+2 = 23 are prime; for p = 67, p^2+4 = 4493 and p^2+4p+2 = 4759 are prime.

%p a := proc (n) if isprime(n) = true and isprime(n^2+4) = true and isprime(n^2+4*n+2) = true then n else end if end proc: seq(a(n), n = 1 .. 7000); # _Emeric Deutsch_, Jan 02 2009

%t Select[Prime[Range[10000]],PrimeQ[#^2+4]&&PrimeQ[#^2 +4#+2]&] (* _Vincenzo Librandi_, Jul 27 2012 *)

%o (Magma) [ p: p in PrimesUpTo(7000) | IsPrime(p^2+4) and IsPrime(p^2+4*p+2) ];

%Y Cf. A062324 (p and p^2+4 are both prime).

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Dec 30 2008

%E Edited, corrected (three terms deleted) and extended beyond a(10) by _Klaus Brockhaus_, Jan 02 2009

%E Corrected and extended by _Emeric Deutsch_, Jan 02 2009