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Search: id:A103231
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| A103231 |
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After the first two terms, each subsequent term is the smallest integer that is an outlier of the previous dataset, based on the criterion of 3 sample standard deviations above the mean. |
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+0
2
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| 1, 2, 4, 7, 12, 19, 29, 42, 59, 80, 107, 140, 180, 228, 285, 351, 429, 519, 622, 740, 874, 1025, 1195, 1385, 1597, 1832, 2092, 2379, 2695, 3041, 3419, 3831, 4279, 4766, 5293, 5862, 6476, 7137, 7847, 8609, 9425, 10298, 11230, 12224, 13282, 14407, 15603
(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 depends on the initial two values and the definition of outlier: whether to use the sample or population standard deviation and how many standard deviations above the mean.
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FORMULA
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a(n) = int(m(n-1) + 3s(n-1) + 1), where m(n-1) is the arithmetic mean of the first n-1 terms and s(n-1) is the sample standard deviation of the first n-1 terms
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EXAMPLE
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a(5) = 12 because the mean of the first 4 terms is 3.5 and the sample standard deviation is 2.65, so the lower limit to any outlier is 11.45 and the next higher integer is 12.
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CROSSREFS
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Cf. A103232.
Sequence in context: A066699 A087149 A090853 this_sequence A002622 A035301 A035297
Adjacent sequences: A103228 A103229 A103230 this_sequence A103232 A103233 A103234
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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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