cp's OEIS Frontend

A353321 a(n) = floor(1/erfc(n/sqrt(2))).

%I A353321 #33 Aug 15 2022 04:58:43
%S A353321 1,3,21,370,15787,1744277,506797345,390682215445,803734397655347,
%T A353321 4430313100526836692,65618063552490194383194,
%U A353321 2616897361902846669558232537,281455127862349591601857362987343,81737217988908649002650313009555641846,64155724364921456082725604130103414484969173
%N A353321 a(n) = floor(1/erfc(n/sqrt(2))).
%C A353321 a(n) is the residual (inverted) of the standard normal distribution in two-sided range of n sigma.
%C A353321 The 1/sqrt(2) factor appears in the argument of the erfc function because the standard normal cumulative distribution function has integrand exp(-(1/2)(x/sigma)^2).
%C A353321 The n=5 value, a(5)=1744277, appeared in discussions of the 5-sigma (two-sided probability) discovery of the Higgs boson at CERN (see articles in Links).
%H A353321 E. Lamb, <a href="https://blogs.scientificamerican.com/observations/five-sigmawhats-that/">Five sigma what's that?</a>
%H A353321 C. Pease, <a href="https://medium.com/@chris.m.pease/the-higgs-boson-and-5-sigma-eec238b43f93">The Higgs Boson and 5 Sigma</a>
%H A353321 D. Spiegelhalter, <a href="https://understandinguncertainty.org/higgs-it-one-sided-or-two-sided">Higgs: is it one-sided or two-sided?</a>
%F A353321 Straightforward asymptotics of erfc (e.g., see Abramowitz and Stegun) gives leading order as a(n) ~ sqrt(Pi/2)*n*exp((1/2)*n^2).
%e A353321 For n=2, a(2)=21 corresponds roughly to the statement that 95.5% of normally distributed measurements fall into the range of two sigma (plus and minus), since 1/21 = 1-0.955 (approximately). Nearest-integer version (A275366) is always more accurate (e.g., a(2)=22).
%t A353321 Table[Floor[1/Erfc[n/Sqrt[2]]], {n, 1, 16}]
%Y A353321 Cf. A275366 (rounded).
%K A353321 nonn
%O A353321 0,2
%A A353321 _Greg Huber_, Jul 04 2022