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URL: https://oeis.org/A069142

⇱ A069142 - OEIS

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A069142
Primes p such that p+2, 2p+1, and 2p+3 are also prime.
8
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
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. A066388.
Sequence in context: A176680 A352948 A352951 * A144994 A263369 A072880
KEYWORD
nonn,easy
AUTHOR
Neil Fernandez, Apr 08 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 11 2002
STATUS
approved