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A273977 Words of length n over an alphabet of size 9 that are in standard order with at least one letter is 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 (list; graph; refs; listen; history; text; internal format)
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 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.

REFERENCES

D. D. 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.

LINKS

Daniel Devatman Hromada, List of n, a(n) for n = 1..142407 (All words with at most 10 digits.)

Joerg Arndt and N. J. A. Sloane, Counting Words that are in "Standard Order"

MATHEMATICA

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

PROG

(PERL)

# script brute-force checking all integers up to infinity

$i=0;

INCREMENT : while ($i) {

$i++;

my %d;

$d{"0"}=1;

$r=0;

for $d (split //, $i) {

next INCREMENT if !exists $d{($d-1)};

if ($d{$d}) {

$r=1;

}

$d{$d}=true;

}

print "$i\n" if $r;

}

CROSSREFS

Cf. A278987.

Sequence in context: A327992 A204847 A098759 * A135464 A231872 A308365

Adjacent sequences:  A273974 A273975 A273976 * A273978 A273979 A273980

KEYWORD

base,easy,nonn

AUTHOR

Daniel Devatman Hromada, Nov 10 2016

EXTENSIONS

Edited by N. J. A. Sloane, Dec 06 2016

Duplicated terms removed from b-file by Andrew Howroyd, Feb 27 2018

STATUS

approved

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Last modified October 22 21:23 EDT 2021. Contains 348180 sequences. (Running on oeis4.)