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A217566 The only prime p such that 4a < p < 4b where a, b are consecutive primes. 8
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).

Sequence in context: A126199 A096342 A066179 * A278869 A272628 A141093

Adjacent sequences:  A217563 A217564 A217565 * A217567 A217568 A217569

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 06 2012

STATUS

approved

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Last modified July 12 06:46 EDT 2020. Contains 335658 sequences. (Running on oeis4.)