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, 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

Offset

1,1

Comments

Conjecture: a(n)>0 for all n.

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Vladimir Shevelev, Ramanujan and Labos Primes, Their Generalizations, and Classifications of Primes, Journal of Integer Sequences, Vol. 15 (2012), Article 12.5.4.

Jonathan Sondow, John W. Nicholson, and Tony D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq., Vol. 14 (2011), Article 11.6.2; arXiv preprint, arXiv:1105.2249 [math.NT], 2011.

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