%I #14 Oct 08 2012 08:53:32

%S 11,23,47,167,409,719,769,907,911,1129,1249,1259,1327,1759,1831,1847,

%T 2179,2281,2399,2473,2579,3313,3413,3433,3449,3761,3967,4079,4201,

%U 4373,4861,4919,5113,5119,5209,5227,5449,5623,5711,5717,5807,5927,5939,5953,6173

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

%C 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.

%C 4-isolated primes according to the classification given in the paper on link (see Section 10). - _Vladimir Shevelev_, Oct 07 2012

%H Zak Seidov, <a href="/A217566/b217566.txt">Table of n, a(n) for n = 1..2000</a>

%H V. Shevelev, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL15/Shevelev/shevelev19.html">Ramanujan and Labos primes, their generalizations, and classifications of primes</a>, J. Integer Seq. 15 (2012) Article 12.5.4

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

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

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

%t 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

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

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 06 2012