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A103231
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.
1
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
OFFSET
1,2
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.
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
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.
CROSSREFS
Cf. A103232.
Sequence in context: A090853 A333311 A266464 * A002622 A363276 A035301
KEYWORD
easy,nonn
AUTHOR
Kerry Mitchell, Jan 26 2005
STATUS
approved