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

1,1

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(Magma) [p: p in PrimesUpTo(160000) | IsPrime(p+2) and IsPrime(2*p+1) and IsPrime(2*p+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

Crossrefs

Cf. A014574.

Cf. A005384, A005382.

Cf. A066388.

Sequence in context: A176680 A352948 A352951 * A144994 A263369 A072880

Adjacent sequences: A069139 A069140 A069141 * A069143 A069144 A069145

Keyword

nonn,easy

Author

Neil Fernandez, Apr 08 2002

Extensions

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

Status

approved