A217561 The only prime p such that 3a < p < 3b where a, b are consecutive primes.

7, 37, 53, 89, 113, 127, 211, 293, 307, 449, 541, 577, 587, 593, 683, 691, 719, 797, 839, 929, 937, 1259, 1297, 1399, 1471, 1499, 1567, 1709, 1777, 1801, 1811, 1847, 1973, 1979, 2039, 2221, 2467, 2503, 2579, 2633, 2647, 2819, 2939, 3037, 3061, 3109, 3187, 3271

Offset: 1

Author

Zak Seidov, Oct 06 2012

Keywords

• nonn

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

Examples

			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].
		

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

Crossrefs

Cf. A166251 (k=2).

Programs

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 *)