

A137670


Prime numbers p such that pb < pa < p < p+a < p+b are prime for some a and b.


0



17, 23, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313
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OFFSET

1,1


COMMENTS

It seems highly likely that all primes other than 2,3,5,7,19 are in this sequence. There are no further exceptions to 4 billion.  Charles R Greathouse IV, Apr 19 2010


LINKS

Table of n, a(n) for n=1..57.


MATHEMATICA

s=""; q=1; For[i=2, i<10^2, p=Prime[i]; For[a=2, a<p, If[PrimeQ[pa]&&PrimeQ[p+a], For[b=a+2, b<p, If[PrimeQ[pb]&&PrimeQ[p+b], For[c=b+2, c<p, If[p>q&&PrimeQ[pc]&&PrimeQ[p+c], (*Print[p, ":", a, ", ", b, ", ", c]; *)s=s<>ToString[p]<>", "; q=p]; c=c+2]]; b=b+2]]; a=a+2]; i++ ]; Print[s]


CROSSREFS

Cf. A071681.
Sequence in context: A050712 A068581 A166864 * A217044 A145484 A080830
Adjacent sequences: A137667 A137668 A137669 * A137671 A137672 A137673


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Apr 27 2008; corrected May 02 2008


EXTENSIONS

New name from Charles R Greathouse IV, Apr 19 2010


STATUS

approved



