A275366 Nearest integer to 1/erfc(n/sqrt(2)).

1, 3, 22, 370, 15787, 1744278, 506797346, 390682215445, 803734397655348, 4430313100526836693, 65618063552490194383194, 2616897361902846669558232538, 281455127862349591601857362987344, 81737217988908649002650313009555641847, 64155724364921456082725604130103414484969173

Offset

0,2

Comments

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.

Links

G. C. Greubel, Table of n, a(n) for n = 0..67

Wikipedia, 68-95-99.7 rule

Formula

a(n) = round( 1/erfc(n/sqrt(2)) ).

Example

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.

Mathematica

Table[Round[1/Erfc[n/Sqrt[2]]], {n, 1, 16}]

Prog

(PARI) default(realprecision, 100); for(n=1, 20, print1(round(1/erfc(n/sqrt(2))), ", ")) \\ G. C. Greubel, Oct 07 2018
(Magma) [Round(1/Erfc(n/Sqrt(2))): n in [1..20]]; // G. C. Greubel, Oct 07 2018

Crossrefs

Cf. probabilities of normal variables exceeding mean by n standard deviations: A239382, A239383, A239384, A239385, A239386, A239387.

One-sided result for n sigma: A219337 (nearest integer to 2/erfc(n/sqrt(2))).

Sequence in context: A099750 A219268 A259919 * A196734 A271849 A271850

Adjacent sequences: A275363 A275364 A275365 * A275367 A275368 A275369

Keyword

nonn

Author

Jeremy Tan, Jul 24 2016

Extensions

a(0)=1 prepended by Greg Huber, Jul 05 2022

Status

approved