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A217561 The only prime p such that 3a < p < 3b where a, b are consecutive primes. 10

%I

%S 7,37,53,89,113,127,211,293,307,449,541,577,587,593,683,691,719,797,

%T 839,929,937,1259,1297,1399,1471,1499,1567,1709,1777,1801,1811,1847,

%U 1973,1979,2039,2221,2467,2503,2579,2633,2647,2819,2939,3037,3061,3109,3187,3271

%N The only prime p such that 3a < p < 3b 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 3-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="/A217561/b217561.txt">Table of n, a(n) for n = 1..1000</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 7 is the only prime in the interval [3*2, 3*3] = [6,9],

%e 37 is the only prime in the interval [3*11, 3*13] = [33,39],

%e 53 is the only prime in the interval [3*17, 3*19] = [51,57].

%t 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

%t NextPrime/@Transpose[Select[3*Partition[Prime[Range[200]],2,1], NextPrime[ #[[1]]] == NextPrime[#[[2]],-1]&]][[1]] (* _Harvey P. Dale_, Oct 12 2012 *)

%Y Cf. A166251 (k=2).

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 06 2012

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Last modified November 29 23:12 EST 2020. Contains 338779 sequences. (Running on oeis4.)