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

1,1

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

Cf. A166251 (k=2).

Sequence in context: A077720 A235463 A127313 * A003521 A155943 A078626

Adjacent sequences: A217558 A217559 A217560 * A217562 A217563 A217564

Keyword

nonn

Author

Zak Seidov, Oct 06 2012

Status

approved