

A161723


Middle members p of prime triples (p18,p,p+18).


4



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
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OFFSET

1,1


COMMENTS

The three primes p18, p and p+18 are not necessarily consecutive.
Solutions of the equation (n18)' + n' + (n+18)' = 3, where n' is the arithmetic derivative of n. [Paolo P. Lava, Nov 08 2012]


LINKS

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


FORMULA

{p: p in A153418 and p18 in A153418}  R. J. Mathar, Sep 22 2009


EXAMPLE

23 is the middle in the triple of three primes (2318=5, 23, 23+18=41) with arithmetic progression 18.


MATHEMATICA

q=6*3; lst={}; Do[p=Prime[n]; If[PrimeQ[pq] && PrimeQ[p+q], AppendTo[lst, p]], {n, 5000}]; lst


CROSSREFS

Cf. A006489, A137796.
Sequence in context: A227757 A227756 A007637 * A085448 A095077 A106989
Adjacent sequences: A161720 A161721 A161722 * A161724 A161725 A161726


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Jun 17 2009


EXTENSIONS

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


STATUS

approved



