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Search: id:A103232
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| A103232 |
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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. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Outlier
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A103231.
Sequence in context: A117143 A115001 A008766 this_sequence A062684 A033485 A026811
Adjacent sequences: A103229 A103230 A103231 this_sequence A103233 A103234 A103235
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KEYWORD
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easy,nonn
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AUTHOR
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Kerry Mitchell (lkmitch(AT)att.net), Jan 26 2005
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