

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
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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

D. D. 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

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 bruteforce 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 $d{($d1)};
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 bfile by Andrew Howroyd, Feb 27 2018


STATUS

approved



