cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A239382 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than one standard deviation.

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%I A239382 #22 Jun 13 2022 16:33:24
%S A239382 1,5,8,6,5,5,2,5,3,9,3,1,4,5,7,0,5,1,4,1,4,7,6,7,4,5,4,3,6,7,9,6,2,0,
%T A239382 7,7,5,2,2,0,8,7,0,3,3,2,7,3,3,9,5,6,0,9,0,1,2,6,0,5,5,4,9,7,5,7,0
%N A239382 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than one standard deviation.
%C A239382 The probability P{(x-m)/s > 1} for a normally distributed random variable x with mean m and standard deviation s.
%C A239382 In experimental sciences (hypothesis testing), a measured excursion exceeding background "noise" by just one standard deviation is not significant, unless corroborated by strong additional indications.
%H A239382 Stanislav Sykora, <a href="/A239382/b239382.txt">Table of n, a(n) for n = 0..2000</a>
%H A239382 Wikipedia, <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
%F A239382 P{(x-m)/s > 1} = P{(x-m)/s < -1} = 0.5*erfc(1/sqrt(2)) = erfc(sqrt(2)/2)/2, with erfc(x) being the complementary error function.
%e A239382 0.15865525393145705141476745436796207752208703327339560901260...
%t A239382 First[RealDigits[1 - CDF[NormalDistribution[], 1], 10, 100]] (* _Joan Ludevid_, Jun 13 2022 *)
%o A239382 (PARI) n=1;a=0.5*erfc(n/sqrt(2))  \\ Use sufficient realprecision
%Y A239382 Cf. P{(x-m)/s>n}: A239383 (n=2), A239384 (n=3), A239385 (n=4), A239386 (n=5), A239387 (n=6).
%K A239382 nonn,cons
%O A239382 0,2
%A A239382 _Stanislav Sykora_, Mar 17 2014