A107578 - OEIS

%I #35 Jul 16 2024 12:38:14

%S 2,3,5,10,25,31,100,155,190,218,1184,1832,2226,3386,14358,30803,31546,

%T 40934,103521,104072,149690,325853,1094422,1319946,2850175,6957877,

%U 10539433,10655463,20684333,23163299,64955635,72507381

%N Prime index of A000101(n), maximal gap upper end prime index.

%C Conjecture: log a(n) ~ n/2. That is, record prime gaps occur about twice as often as records in an i.i.d. random sequence of comparable length (see arXiv:1709.05508 for a heuristic explanation). - _Alexei Kourbatov_, Jan 18 2019

%H John W. Nicholson, <a href="/A107578/b107578.txt">Table of n, a(n) for n = 1..80</a> (terms 1..75 from Jens Kruse Andersen; further terms coming from Thomas R. Nicely site).

%H Alex Beveridge, <a href="/A107578/a107578.txt">Table giving known values of A000101(n), A005250(n), A107578(n)</a>

%H Alexei Kourbatov, <a href="https://arxiv.org/abs/1709.05508">On the nth record gap between primes in an arithmetic progression</a>, arXiv:1709.05508 [math.NT], 2017; <a href="https://doi.org/10.12988/imf.2018.712103">Int. Math. Forum, 13 (2018), 65-78</a>.

%H Alexei Kourbatov and Marek Wolf, <a href="https://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv:1901.03785 [math.NT], 2019.

%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a>

%H Thomas R. Nicely, <a href="/A000101/a000101.pdf">First occurrence prime gaps</a> [Local copy, pdf only]

%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/index.html">Some Results of Computational Research in Prime Numbers</a> [See local copy in A007053]

%H Matt Visser, <a href="https://arxiv.org/abs/1904.00499">Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap</a>, arXiv:1904.00499 [math.NT], 2019.

%F a(n) = A005669(n)+1. - _Jens Kruse Andersen_, Oct 19 2010

%F From _John W. Nicholson_, Oct 29 2021: (Start)

%F a(n) = A000720(A000101(n)).

%F a(n) = A000720(A002386(n)) + 1. (End)

%e The prime index of a(3) = 5, so prime(a(3)) = prime(5) = 11.

%Y Cf. A000101, A005250, A002386, A005669.

%K nonn

%O 1,1

%A Alex Beveridge, Apr 25 2007

%E Name modified by _John W. Nicholson_, Nov 19 2013