A107578 Prime index of A000101(n), maximal gap upper end prime index.

2, 3, 5, 10, 25, 31, 100, 155, 190, 218, 1184, 1832, 2226, 3386, 14358, 30803, 31546, 40934, 103521, 104072, 149690, 325853, 1094422, 1319946, 2850175, 6957877, 10539433, 10655463, 20684333, 23163299, 64955635, 72507381

Offset: 1

Author

Alex Beveridge, Apr 25 2007

Keywords

• nonn

Comments

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

Examples

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

Links

• John W. Nicholson, Table of n, a(n) for n = 1..80 (terms 1..75 from Jens Kruse Andersen; further terms coming from Thomas R. Nicely site).
• Alex Beveridge, Table giving known values of A000101(n), A005250(n), A107578(n)
• Alexei Kourbatov, On the nth record gap between primes in an arithmetic progression, arXiv:1709.05508 [math.NT], 2017; Int. Math. Forum, 13 (2018), 65-78.
• Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv:1901.03785 [math.NT], 2019.
• Thomas R. Nicely, First occurrence prime gaps
• Thomas R. Nicely, First occurrence prime gaps [Local copy, pdf only]
• Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
• Matt Visser, Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap, arXiv:1904.00499 [math.NT], 2019.

Crossrefs

Cf. A000101, A005250, A002386, A005669.

Formula

a(n) = A005669(n)+1. - Jens Kruse Andersen, Oct 19 2010

From John W. Nicholson, Oct 29 2021: (Start)

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

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

Extensions

Name modified by John W. Nicholson, Nov 19 2013