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 A218279 Let (p(n), p(n)+2) be the n-th twin prime pair. a(n) is the smallest k, such that there is only one prime in the interval (k*p(n), k*(p(n)+2)), or a(n)=0, if there is no such k. 2
 2, 4, 2, 2, 3, 2, 6, 5, 3, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 5, 2, 2, 4, 3, 3, 2, 2, 2, 3, 6, 3, 2, 4, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 5, 2, 2, 2, 3, 2, 3, 3, 6, 3, 4, 9, 5, 2, 5, 4, 2, 3, 2, 3, 3, 2, 4, 3, 2, 2, 5, 3, 4, 4, 4, 4, 3, 2, 6, 2, 7, 4, 2, 6, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: a(n)>0 for all n. LINKS Zak Seidov, Table of n, a(n) for n = 1..10000 V. Shevelev, Ramanujan and Labos Primes, Their Generalizations, and Classifications of Primes, Journal of Integer Sequences, Vol. 15 (2012), Article 12.5.4 J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2 EXAMPLE The first pair of twin primes is (3,5). For k=1 and 2, we have the intervals (3,5) and (6,10), such that not the first but the second interval contains exactly one prime(7). Thus a(1)=2. For n=2 and k=1 to 4, we have the intervals (5,7),(10,14),(15,21), and (20,28) and only the last interval contains exactly one prime(23). Thus, a(2)=4. CROSSREFS Cf. A218275, A166251, A217561, A217566, A217577, A001359, A014574, A006512, A077800. Sequence in context: A286479 A013604 A218217 * A183193 A331470 A021809 Adjacent sequences:  A218276 A218277 A218278 * A218280 A218281 A218282 KEYWORD nonn AUTHOR Vladimir Shevelev, Oct 25 2012 EXTENSIONS a(6) corrected and terms beyond a(11) contributed by Zak Seidov, Oct 25 2012 STATUS approved

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Last modified December 3 04:53 EST 2021. Contains 349445 sequences. (Running on oeis4.)