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 A005669 Indices of primes where largest gap occurs. (Formerly M1193) 29
 1, 2, 4, 9, 24, 30, 99, 154, 189, 217, 1183, 1831, 2225, 3385, 14357, 30802, 31545, 40933, 103520, 104071, 149689, 325852, 1094421, 1319945, 2850174, 6957876, 10539432, 10655462, 20684332, 23163298, 64955634, 72507380, 112228683 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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, Mar 28 2018 REFERENCES H. Riesel, Prime numbers and computer methods for factorization, Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..77 Jens Kruse Andersen, The Top-20 Prime Gaps Jens Kruse Andersen, New record prime gap Jens Kruse Andersen, Maximal gaps R. K. Guy, Letter to N. J. A. Sloane, 1987 Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053 [math.NT], 2013. 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 preprint arXiv:1901.03785 [math.NT], 2019. Matt Visser, Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap, arXiv:1904.00499 [math.NT], 2019. R. G. Wilson, V, Notes (no date) J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224. FORMULA a(n) = A000720(A002386(n)). a(n) = A107578(n) - 1. - Jens Kruse Andersen, Oct 19 2010 MATHEMATICA 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 *) CROSSREFS Cf. A000101, A002386, A005250. Sequence in context: A229048 A144309 A080376 * A038664 A261367 A148077 Adjacent sequences:  A005666 A005667 A005668 * A005670 A005671 A005672 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)