

A273977


Words over an alphabet of size 9 that are in standard order with at least one letter repeated.


3



11, 111, 112, 121, 122, 1111, 1112, 1121, 1122, 1123, 1211, 1212, 1213, 1221, 1222, 1223, 1231, 1232, 1233, 11111, 11112, 11121, 11122, 11123, 11211, 11212, 11213, 11221, 11222, 11223, 11231, 11232, 11233, 11234, 12111, 12112, 12113, 12121, 12122, 12123, 12131, 12132, 12133, 12134, 12211, 12212
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OFFSET

1,1


COMMENTS

We study words made of letters from an alphabet of size b, where b >= 1. (Here b=9.) We assume the letters are labeled {1,2,3,...,b}. There are b^n possible words of length n.
We say that a word is in "standard order" if it has the property that whenever a letter i appears, the letter i1 has already appeared in the word. This implies that all words begin with the letter 1.
These are the words described in row b=9 of the array in A278986.
This sequence can be potentially expanded by a much more efficient algorithm than the bruteforce one presented in the program section.


REFERENCES

Daniel Devatman Hromada, Integerbased nomenclature for the ecosystem of repetitive expressions in complete works of William Shakespeare, submitted to special issue of Argument and Computation on Rhetorical Figures in Computational Argument Studies, 2016.


LINKS



MATHEMATICA

Select[Range[2*10^4], And[Max[DigitCount@ #] >= 2, Range@ Length@ Union@ # == DeleteDuplicates@ # &@ IntegerDigits@ #] &] (* Michael De Vlieger, Nov 10 2016 *)


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



