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%I M1193 #86 Nov 06 2023 03:34:44
%S 1,2,4,9,24,30,99,154,189,217,1183,1831,2225,3385,14357,30802,31545,
%T 40933,103520,104071,149689,325852,1094421,1319945,2850174,6957876,
%U 10539432,10655462,20684332,23163298,64955634,72507380,112228683,182837804,203615628,486570087
%N Indices of primes where largest gap occurs.
%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_, Mar 28 2018
%D H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, Chap. 4, see pp. 381-384.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H John W. Nicholson, <a href="/A005669/b005669.txt">Table of n, a(n) for n = 1..80</a> (added data from Thomas R. Nicely site; first 77 terms from Charles R Greathouse IV)
%H Jens Kruse Andersen, <a href="http://primerecords.dk/primegaps/gaps20.htm">The Top-20 Prime Gaps</a>.
%H Jens Kruse Andersen, <a href="http://primerecords.dk/primegaps/megagap2.htm">New record prime gap</a>.
%H Jens Kruse Andersen, <a href="http://primerecords.dk/primegaps/maximal.htm">Maximal gaps</a>.
%H R. K. Guy, <a href="/A005667/a005667.pdf">Letter to N. J. A. Sloane, 1987</a>.
%H Alexei Kourbatov, <a href="http://arxiv.org/abs/1309.4053">Tables of record gaps between prime constellations</a>, arXiv preprint arXiv:1309.4053 [math.NT], 2013.
%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="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint 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>. [For local copy see A000101]
%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.
%H Robert G. Wilson v, <a href="/A005250/a005250.pdf">Notes (no date)</a>.
%H J. Young and A. Potler, <a href="http://dx.doi.org/10.1090/S0025-5718-1989-0947470-1">First occurrence prime gaps</a>, Math. Comp., 52 (1989), 221-224.
%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F a(n) = A000720(A002386(n)).
%F a(n) = A107578(n) - 1. - _Jens Kruse Andersen_, Oct 19 2010
%t f[n_] := Block[{d, i, m = 0}, Reap@ For[i = 1, i <= n, i++, d = Prime[i + 1] - Prime@ i; If[d > m, m = d; Sow@ i, False]] // Flatten // Rest]; f@ 1000000 (* _Michael De Vlieger_, Mar 24 2015 *)
%Y Cf. A000101, A002386, A005250.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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