

A113275


Lesser of twin primes for which the gap before the following twin primes is a record.


6



3, 5, 17, 41, 71, 311, 347, 659, 2381, 5879, 13397, 18539, 24419, 62297, 187907, 687521, 688451, 850349, 2868959, 4869911, 9923987, 14656517, 17382479, 30752231, 32822369, 96894041, 136283429, 234966929, 248641037, 255949949
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OFFSET

1,1


LINKS

Martin Raab, Table of n, a(n) for n = 1..82 (first 75 terms from Max Alekseyev)
Alexei Kourbatov, Maximal gaps between prime ktuples: a statistical approach, arXiv preprint arXiv:1301.2242 [math.NT], 2013.
Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053 [math.NT], 2013.
Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
Mersenneforum, Gaps between prime pairs (Twin Primes).
Tomás Oliveira e Silva, Gaps between twin primes


FORMULA

a(n) = A036061(n)  2.
a(n) = A036062(n)  A113274(n).


EXAMPLE

The smallest twin prime pair is 3, 5, then 5, 7 so a(1) = 3; the following pair is 11, 13 so a(2) = 5 because 11  5 = 6 > 5  3 = 2; the following pair is 17, 19: since 17  11 = 6 = 11  5 nothing happens; the following pair is 29, 31 so a(3)= 17 because 29  17 = 12 > 11  5 = 6.


MATHEMATICA

NextLowerTwinPrim[n_] := Block[{k = n + 2}, While[ !PrimeQ[k]  !PrimeQ[k + 2], k++ ]; k]; p = 3; r = 0; t = {3}; Do[q = NextLowerTwinPrim[p]; If[q > r + p, AppendTo[t, p]; r = q  p]; p = q, {n, 10^9}] (* Robert G. Wilson v, Oct 22 2005 *)


CROSSREFS

Record gaps are given in A113274. Cf. A002386.
Sequence in context: A308588 A141160 A336380 * A280080 A001572 A236458
Adjacent sequences: A113272 A113273 A113274 * A113276 A113277 A113278


KEYWORD

nonn


AUTHOR

Bernardo Boncompagni, Oct 21 2005


EXTENSIONS

a(22)a(30) from Robert G. Wilson v, Oct 22 2005
Terms up to a(72) are listed in Kourbatov (2013), terms up to a(75) in Oliveira e Silva's website, added by Max Alekseyev, Nov 06 2015


STATUS

approved



