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A107578
Prime index of A000101(n), maximal gap upper end prime index.
4
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
1,1
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
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).
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]
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)
EXAMPLE
The prime index of a(3) = 5, so prime(a(3)) = prime(5) = 11.
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Beveridge, Apr 25 2007
EXTENSIONS
Name modified by John W. Nicholson, Nov 19 2013
STATUS
approved