A217566 - OEIS

A217566

The only prime p such that 4a < p < 4b where a, b are consecutive primes.

11, 23, 47, 167, 409, 719, 769, 907, 911, 1129, 1249, 1259, 1327, 1759, 1831, 1847, 2179, 2281, 2399, 2473, 2579, 3313, 3413, 3433, 3449, 3761, 3967, 4079, 4201, 4373, 4861, 4919, 5113, 5119, 5209, 5227, 5449, 5623, 5711, 5717, 5807, 5927, 5939, 5953, 6173

(list; graph; refs; listen; history; text; internal format)

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.

4-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..2000

V. Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012) Article 12.5.4

EXAMPLE

11 is the only prime in the interval [4*2, 4*3] = [8,12],

23 is the only prime in the interval [4*5, 4*7] = [20,28],

47 is the only prime in the interval [4*11, 4*13] = [44,52].

MATHEMATICA

a = 2; b = 3; s = {}; k = 4; Do[If[(p=NextPrime[k*a]) < k*b && NextPrime[p] > k*b, AppendTo[s, p]]; a = b; b = NextPrime[b], {100}]; s

CROSSREFS

Cf. A166251 (k=2), A217561 (k=3).