A137670 Prime numbers p such that p-b < p-a < p < p+a < p+b are prime for some a and b.

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

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[p-a]&&PrimeQ[p+a], For[b=a+2, b<p, If[PrimeQ[p-b]&&PrimeQ[p+b], For[c=b+2, c<p, If[p>q&&PrimeQ[p-c]&&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 * A330600 A217044 A145484

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