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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, 182837804, 203615628, 486570087 (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, Birkhäuser, 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
John W. Nicholson, Table of n, a(n) for n = 1..80 (added data from Thomas R. Nicely site; first 77 terms from Charles R Greathouse IV)
Jens Kruse Andersen, The Top-20 Prime Gaps.
Jens Kruse Andersen, New record prime gap.
Jens Kruse Andersen, Maximal gaps.
Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053 [math.NT], 2013.
Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.
Thomas R. Nicely, First occurrence prime gaps. [For local copy see A000101]
Robert 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
Sequence in context: A229048 A144309 A080376 * A038664 A261367 A148077
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)