OFFSET
0,2
COMMENTS
a(n) is the residual (inverted) of the standard normal distribution in two-sided range of n sigma.
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).
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).
LINKS
E. Lamb, Five sigma what's that?
C. Pease, The Higgs Boson and 5 Sigma
D. Spiegelhalter, Higgs: is it one-sided or two-sided?
FORMULA
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).
EXAMPLE
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).
MATHEMATICA
Table[Floor[1/Erfc[n/Sqrt[2]]], {n, 1, 16}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Greg Huber, Jul 04 2022
STATUS
approved