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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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
| 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
| Cf. A103232.
Sequence in context: A188425 A087149 A090853 * A002622 A035301 A035297
Adjacent sequences: A103228 A103229 A103230 * A103232 A103233 A103234
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KEYWORD
| easy,nonn
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AUTHOR
| Kerry Mitchell (lkmitch(AT)att.net), Jan 26 2005
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