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A273977
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Words over an alphabet of size 9 that are in standard order with at least one letter repeated.
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3
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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
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1,1
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COMMENTS
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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 i-1 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 brute-force one presented in the program section.
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REFERENCES
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Daniel Devatman Hromada, Integer-based 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.
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LINKS
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MATHEMATICA
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Select[Range[2*10^4], And[Max[DigitCount@ #] >= 2, Range@ Length@ Union@ # == DeleteDuplicates@ # &@ IntegerDigits@ #] &] (* Michael De Vlieger, Nov 10 2016 *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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