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 A278987.
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, Table of n, a(n) for n = 1..4360
Joerg Arndt and N. J. A. Sloane, Counting Words that are in "Standard Order"
PROG
#PERL checking whether numbers listed in A273977 and given in standard input belong to the current sequence
OUTER: while (<>) {
my %d;
$i=$_;
chop $i;
for $d (split //, $i) {
(exists $d{$d}) ? ($d{$d}++) : ($d{$d}=1);
}
for $k (keys %d) {
next OUTER if ($d{$k}<2);
}
print "$i\n";
}
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Daniel Devatman Hromada, Nov 10 2016
EXTENSIONS
Edited by N. J. A. Sloane, Dec 06 2016
STATUS
approved