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 A217561 The only prime p such that 3a < p < 3b where a, b are consecutive primes. 10
 7, 37, 53, 89, 113, 127, 211, 293, 307, 449, 541, 577, 587, 593, 683, 691, 719, 797, 839, 929, 937, 1259, 1297, 1399, 1471, 1499, 1567, 1709, 1777, 1801, 1811, 1847, 1973, 1979, 2039, 2221, 2467, 2503, 2579, 2633, 2647, 2819, 2939, 3037, 3061, 3109, 3187, 3271 (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. 3-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..1000 V. Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012) Article 12.5.4 EXAMPLE 7 is the only prime in the interval [3*2, 3*3] = [6,9], 37 is the only prime in the interval [3*11, 3*13] = [33,39], 53 is the only prime in the interval [3*17, 3*19] = [51,57]. MATHEMATICA 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 NextPrime/@Transpose[Select[3*Partition[Prime[Range[200]], 2, 1], NextPrime[ #[[1]]] == NextPrime[#[[2]], -1]&]][[1]] (* Harvey P. Dale, Oct 12 2012 *) CROSSREFS Cf. A166251 (k=2). Sequence in context: A077720 A235463 A127313 * A003521 A155943 A078626 Adjacent sequences:  A217558 A217559 A217560 * A217562 A217563 A217564 KEYWORD nonn AUTHOR Zak Seidov, Oct 06 2012 STATUS approved

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Last modified October 27 01:02 EDT 2020. Contains 338035 sequences. (Running on oeis4.)