

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
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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, Birkhäuser, 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



FORMULA



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



KEYWORD

nonn


AUTHOR



STATUS

approved



