cp's OEIS Frontend

A069142 Primes p such that p+2, 2p+1, and 2p+3 are also prime.

%I A069142 #28 Nov 02 2023 07:49:07
%S A069142 5,29,659,809,2129,2549,3329,3389,5849,6269,10529,33179,41609,44129,
%T A069142 53549,55439,57329,63839,65099,70379,70979,72269,74099,74759,78779,
%U A069142 80669,81929,87539,93239,102299,115469,124769,133979,136949,156419
%N A069142 Primes p such that p+2, 2p+1, and 2p+3 are also prime.
%C A069142 Previous name: Lower prime in a twin pair that yields another.
%C A069142 a(n) gives the terms for A005382(i)-A005384(j)=2. - _J. M. Bergot_, Mar 12 2015
%H A069142 Vincenzo Librandi, <a href="/A069142/b069142.txt">Table of n, a(n) for n = 1..1000</a>
%F A069142 a(n) = A066388(n)-1. - _R. J. Mathar_, Nov 02 2023
%e A069142 659 and 661 form a prime twin pair. Their sum is 1320. 1320 is sandwiched between 1319 and 1321, which form another prime twin pair. So 659 is in the sequence.
%t A069142 p = q = 1; Do[q = Prime[n]; If[p + 2 == q && PrimeQ[2p + 1] && PrimeQ[2p + 3], Print[p]]; p = q, {n, 1, 10^4}]
%t A069142 Select[Prime[Range[15000]], PrimeQ[# + 2] && PrimeQ[2 # + 1] && PrimeQ[2 # + 3]&] (* _Vincenzo Librandi_, Apr 09 2013 *)
%o A069142 (Magma) [p: p in PrimesUpTo(160000) | IsPrime(p+2) and IsPrime(2*p+1) and IsPrime(2*p+3)]; // _Vincenzo Librandi_, Apr 09 2013
%o A069142 (PARI) forprime(p=1,10^5,if(isprime(p+2)&&isprime(2*p+1)&&isprime(2*p+3),print1(p,", "))) \\ _Derek Orr_, Mar 11 2015
%Y A069142 Cf. A014574.
%Y A069142 Cf. A005384, A005382.
%Y A069142 Cf. A066388.
%K A069142 nonn,easy
%O A069142 1,1
%A A069142 _Neil Fernandez_, Apr 08 2002
%E A069142 Edited and extended by _Robert G. Wilson v_, Apr 11 2002