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A212659 Good's example of a "Standard List" of prime words over the alphabet {1,2}. 2
1, 2, 12, 112, 212, 1112, 2212, 2112, 11112, 21112, 12112, 22112, 12212, 22212, 111112, 211112, 121112, 221112, 122112, 222112, 112212, 122212, 222212, 1111112, 2111112, 1211112, 2211112, 1121112 (list; graph; refs; listen; history; text; internal format)



This is just one possible ordering of the list, given by Good in his Table 1. There are A001037(n) words of length n in the list, and they can be arranged in A001037(n)! ways. However, changing the order would also change the individual entries.

This sequence is well-defined only in the sense that it is in the order chosen by Good, who gives the 71 words of length <= 8. The sequence must be regarded as being undefined beyond that point.

For the rules that the list must satisfy, see pages 28-31 of Good.


Good, I. J. The factorization of a sum of matrices and the multivariate cumulants of a set of quadratic expressions. J. Combinatorial Theory Ser. A 11 1971 27--37. MR0274311 (43 #76)


Table of n, a(n) for n=1..28.

I. J. Good, Annotated scan of page 28

I. J. Good, Annotated scan of page 29

I. J. Good, Annotated scan of page 30

I. J. Good, Annotated scan of part of page 31


Cf. A001037, A212672.

Sequence in context: A317208 A207778 A102659 * A191895 A047855 A199045

Adjacent sequences:  A212656 A212657 A212658 * A212660 A212661 A212662




N. J. A. Sloane, May 23 2012



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Last modified September 26 01:25 EDT 2020. Contains 337346 sequences. (Running on oeis4.)