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, 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

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(n-1) + 1.5*iqr(n-1) + 1), where q3(n-1) is the third quartile of the first n-1 terms and iqr(n-1) is the interquartile range of the first n-1 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: A309408 A347647 A008766 * A062684 A341912 A033485

Adjacent sequences: A103229 A103230 A103231 * A103233 A103234 A103235

Keyword

easy,nonn

Author

Kerry Mitchell, Jan 26 2005

Status

approved