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%I #23 Sep 08 2022 08:46:17
%S 1,3,22,370,15787,1744278,506797346,390682215445,803734397655348,
%T 4430313100526836693,65618063552490194383194,
%U 2616897361902846669558232538,281455127862349591601857362987344,81737217988908649002650313009555641847,64155724364921456082725604130103414484969173
%N Nearest integer to 1/erfc(n/sqrt(2)).
%C Samples from a normally distributed random variable that are at least n standard deviations away from the mean have an approximately 1-in-a(n) chance of occurring.
%H G. C. Greubel, <a href="/A275366/b275366.txt">Table of n, a(n) for n = 0..67</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule">68-95-99.7 rule</a>
%F a(n) = round( 1/erfc(n/sqrt(2)) ).
%e A "five-sigma" event (five standard deviations away from the mean) has a 1 in 1744278 chance of occurring. This is the requirement in particle physics for an anomaly to be recognized as a real effect, not merely a statistical fluctuation.
%t Table[Round[1/Erfc[n/Sqrt[2]]], {n, 1, 16}]
%o (PARI) default(realprecision, 100); for(n=1, 20, print1(round(1/erfc(n/sqrt(2))), ", ")) \\ _G. C. Greubel_, Oct 07 2018
%o (Magma) [Round(1/Erfc(n/Sqrt(2))): n in [1..20]]; // _G. C. Greubel_, Oct 07 2018
%Y Cf. probabilities of normal variables exceeding mean by n standard deviations: A239382, A239383, A239384, A239385, A239386, A239387.
%Y One-sided result for n sigma: A219337 (nearest integer to 2/erfc(n/sqrt(2)).
%K nonn
%O 0,2
%A _Jeremy Tan_, Jul 24 2016
%E a(0)=1 prepended by _Greg Huber_, Jul 05 2022
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