A212659 - OEIS

%I #28 Feb 20 2024 13:18:38

%S 1,2,12,112,212,1112,2212,2112,11112,21112,12112,22112,12212,22212,

%T 111112,211112,121112,221112,122112,222112,112212,122212,222212,

%U 1111112,2111112,1211112,2211112,1121112

%N Good's example of a "Standard List" of prime words over the alphabet {1,2}.

%C 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.

%C 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.

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

%H I. J. Good, <a href="https://doi.org/10.1016/0097-3165(71)90004-5">The factorization of a sum of matrices and the multivariate cumulants of a set of quadratic expressions</a>, J. Combinatorial Theory Ser. A 11 1971 27--37. MR0274311 (43 #76).

%H I. J. Good, <a href="/A212659/a212659.jpg">Annotated scan of page 28</a>

%H I. J. Good, <a href="/A212659/a212659_1.jpg">Annotated scan of page 29</a>

%H I. J. Good, <a href="/A212659/a212659_2.jpg">Annotated scan of page 30</a>

%H I. J. Good, <a href="/A212659/a212659_3.jpg">Annotated scan of part of page 31</a>

%Y Cf. A001037, A212672.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 23 2012