A088254 Primes p with property that if p = prime(k), if the product of all composite numbers between prime(k) and prime(k+1) is one less than a prime.

2, 3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 71, 73, 97, 101, 107, 109, 127, 137, 149, 167, 179, 191, 193, 197, 227, 233, 239, 269, 281, 311, 331, 347, 349, 419, 431, 439, 461, 463, 467, 509, 521, 569, 599, 617, 641, 647, 659, 739, 757, 769, 809, 821, 827

Offset

1,1

Comments

Conjecture: the sequence is infinite. The smaller member of the twin prime pairs is a term.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

19 is a member as 20*21*22 +1 = 9241 is a prime.

Mathematica

Transpose[Select[Partition[Prime[Range[200]], 2, 1], PrimeQ[Times@@ Range[ First[#]+1, Last[#]-1]+1]&]][[1]] (* Harvey P. Dale, Oct 31 2011 *)

Crossrefs

Sequence in context: A038933 A042998 A091317 * A089191 A225184 A038947

Adjacent sequences: A088251 A088252 A088253 * A088255 A088256 A088257

Keyword

base,nonn

Author

Amarnath Murthy, Sep 27 2003

Extensions

More terms from David Wasserman, Jul 25 2005

Status

approved