

A103232


After the first two terms, each subsequent term is the smallest integer that is an outlier of the set of the previous terms, based on the criterion of 1.5 interquartile ranges above the third quartile.


1



1, 2, 3, 5, 7, 10, 13, 18, 23, 29, 37, 46, 55, 66, 80, 95, 111, 128, 147, 170, 196, 223, 252, 282, 314, 349, 390, 435, 482, 531, 584, 637, 693, 751, 814, 885, 962, 1045, 1130, 1217, 1309, 1405, 1501, 1601, 1704, 1809, 1924, 2049, 2182
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OFFSET

1,2


COMMENTS

This sequence is dependent upon the initial two terms and how quartiles are defined (e.g., do you include the median) and how many interquartile ranges above the third quartile to go.


LINKS

Table of n, a(n) for n=1..49.
Eric Weisstein's World of Mathematics, Outlier


FORMULA

a(n) = int(q3(n1) + 1.5*iqr(n1) + 1), where q3(n1) is the third quartile of the first n1 terms and iqr(n1) is the interquartile range of the first n1 terms.


EXAMPLE

a(8) = 18 because the third quartile of the first 7 terms is 8.5 and the interquartile range of the first 7 terms is 6, so the lower limit for outliers is 17.5 and the next higher integer is 18.


CROSSREFS

Cf. A103231.
Sequence in context: A319470 A115001 A008766 * A062684 A033485 A026811
Adjacent sequences: A103229 A103230 A103231 * A103233 A103234 A103235


KEYWORD

easy,nonn


AUTHOR

Kerry Mitchell, Jan 26 2005


STATUS

approved



