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

Author

N. J. A. Sloane

Keywords

• nonn

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

Crossrefs

Cf. A036062, A036063, A002386, A113275.

Programs

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 *)

Formula

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

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

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