A161723 Middle members p of prime triples (p-18,p,p+18).

23, 29, 41, 61, 71, 79, 89, 131, 149, 181, 211, 251, 331, 349, 401, 439, 449, 461, 659, 691, 701, 709, 751, 769, 839, 929, 1031, 1051, 1069, 1231, 1301, 1471, 1549, 1601, 1619, 1741, 1759, 1889, 1931, 2011, 2081, 2161, 2221, 2269, 2399, 2441, 2459, 2521

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 17 2009

Keywords

• nonn

Comments

The three primes p-18, p and p+18 are not necessarily consecutive.

Examples

			23 is the middle in the triple of three primes (23-18=5, 23, 23+18=41) with arithmetic progression 18.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006489, A137796.

Programs

Mathematica

q=6*3; lst={}; Do[p=Prime[n]; If[PrimeQ[p-q] && PrimeQ[p+q], AppendTo[lst,p]], {n, 5000}]; lst
Select[Prime[Range[7,400]],AllTrue[#+{18,-18},PrimeQ]&] (* Harvey P. Dale, Apr 21 2024 *)

Formula

{p: p in A153418 and p-18 in A153418} - R. J. Mathar, Sep 22 2009

Extensions

Rephrased the definition - R. J. Mathar, Sep 22 2009