OFFSET
1,1
COMMENTS
Corresponding values of b-a: 1, 2, 2, 2, 4, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 6, 4, 4, 2, 2, 2, 4, 4, 4, 2, 2, 6, 2, 6, 4, 6, 2, 6, 4, 2, 10. In most cases b-a = 2.
3-isolated primes according to the classification given in the paper on link (see Section 10). - Vladimir Shevelev, Oct 07 2012
LINKS
Zak Seidov, Table of n, a(n) for n = 1..1000
V. Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012) Article 12.5.4
EXAMPLE
7 is the only prime in the interval [3*2, 3*3] = [6,9],
37 is the only prime in the interval [3*11, 3*13] = [33,39],
53 is the only prime in the interval [3*17, 3*19] = [51,57].
MATHEMATICA
a = 2; b = 3; s = {}; k = 3; Do[If[(p=NextPrime[k*a])< k*b && NextPrime[p] > k*b, AppendTo[s, p]]; a = b; b = NextPrime[b], {100}]; s
NextPrime/@Transpose[Select[3*Partition[Prime[Range[200]], 2, 1], NextPrime[ #[[1]]] == NextPrime[#[[2]], -1]&]][[1]] (* Harvey P. Dale, Oct 12 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 06 2012
STATUS
approved