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A275366
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Nearest integer to 1/erfc(n/sqrt(2)).
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2
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1, 3, 22, 370, 15787, 1744278, 506797346, 390682215445, 803734397655348, 4430313100526836693, 65618063552490194383194, 2616897361902846669558232538, 281455127862349591601857362987344, 81737217988908649002650313009555641847, 64155724364921456082725604130103414484969173
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = round( 1/erfc(n/sqrt(2)) ).
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EXAMPLE
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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.
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MATHEMATICA
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Table[Round[1/Erfc[n/Sqrt[2]]], {n, 1, 16}]
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PROG
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(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
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CROSSREFS
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One-sided result for n sigma: A219337 (nearest integer to 2/erfc(n/sqrt(2)).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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