A036061 Increasing gaps among twin primes: the largest prime of the starting twin pair.

5, 7, 19, 43, 73, 313, 349, 661, 2383, 5881, 13399, 18541, 24421, 62299, 187909, 687523, 688453, 850351, 2868961, 4869913, 9923989, 14656519, 17382481, 30752233, 32822371, 96894043, 136283431, 234966931, 248641039, 255949951, 390817729, 698542489, 2466641071

Offset

1,1

Comments

Has many terms in common with A054691, but neither of the two is a subsequence of the other one. - M. F. Hasler, May 07 2022

Links

Martin Raab, Table of n, a(n) for n = 1..82

Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Tomás Oliveira e Silva, Gaps between twin primes

Randall Rathbun, Twin Prime Gaps, NMBRTHRY Mailing List, Nov 23 1998.

Eric Weisstein's World of Mathematics, Prime Constellation

Formula

a(n) = A036062(n) - A036063(n).

a(n) = A113275(n) + 2.

Mathematica

Block[{s = Select[Partition[Prime@ Range[10^7], 2, 1], Subtract @@ # == -2 &][[All, -1]], t}, t = Differences@ s; Map[s[[FirstPosition[t, #]]] &, Union@ FoldList[Max, t]][[All, 1]]] (* Michael De Vlieger, Jan 18 2019 *)

Crossrefs

Cf. A036062, A036063, A002386, A113275.

Sequence in context: A342738 A321510 A084198 * A288608 A079361 A162268

Adjacent sequences: A036058 A036059 A036060 * A036062 A036063 A036064

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms 5, 7 prepended by Max Alekseyev, Nov 05 2015

a(17) corrected and a(31)-a(33) from Sean A. Irvine, Oct 21 2020

Status

approved