

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
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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. 381384.
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 Top20 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), 6578.
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), 221224.
Index entries for primes, gaps between


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

N. J. A. Sloane


STATUS

approved



