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

5, 29, 659, 809, 2129, 2549, 3329, 3389, 5849, 6269, 10529, 33179, 41609, 44129, 53549, 55439, 57329, 63839, 65099, 70379, 70979, 72269, 74099, 74759, 78779, 80669, 81929, 87539, 93239, 102299, 115469, 124769, 133979, 136949, 156419

Offset: 1

Author

Neil Fernandez, Apr 08 2002

Keywords

• nonn
• easy

Comments

Previous name: Lower prime in a twin pair that yields another.

a(n) gives the terms for A005382(i)-A005384(j)=2. - J. M. Bergot, Mar 12 2015

Examples

			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.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A014574.

Cf. A005384, A005382.

Cf. A066388.

Programs

Magma

[p: p in PrimesUpTo(160000) | IsPrime(p+2) and IsPrime(2*p+1) and IsPrime(2*p+3)]; // Vincenzo Librandi, Apr 09 2013

Mathematica

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}]
Select[Prime[Range[15000]], PrimeQ[# + 2] && PrimeQ[2 # + 1] && PrimeQ[2 # + 3]&] (* Vincenzo Librandi, Apr 09 2013 *)

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

Formula

a(n) = A066388(n)-1. - R. J. Mathar, Nov 02 2023

Extensions

Edited and extended by Robert G. Wilson v, Apr 11 2002