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

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).

Sequence in context: A126199 A096342 A066179 * A347141 A278869 A272628

Adjacent sequences: A217563 A217564 A217565 * A217567 A217568 A217569

Keyword

nonn

Author

Zak Seidov, Oct 06 2012

Status

approved