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, 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.

Links

Table of n, a(n) for n=1..47.

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

Adjacent sequences: A103228 A103229 A103230 * A103232 A103233 A103234

Keyword

easy,nonn

Author

Kerry Mitchell, Jan 26 2005

Status

approved