

A239019


Numbers which are not primitive words over the alphabet {0,...,9} (when written in base 10).


5



11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1010, 1111, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2020, 2121, 2222, 2323, 2424, 2525, 2626, 2727, 2828, 2929, 3030, 3131, 3232, 3333, 3434, 3535, 3636, 3737, 3838, 3939, 4040, 4141, 4242, 4343, 4444, 4545, 4646, 4747, 4848, 4949
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OFFSET

1,1


COMMENTS

A word is primitive iff it is not a power, i.e., repetition, of a subword. The only nonprimitive words with a prime number of letters (here: digits) are the repdigit numbers. Thus, the first nontrivial terms of this sequence are 1010,1212,...
This sequence does *not* contain all nonprimitive words over the alphabet {0,...,9}, namely, it excludes those which would be numbers with leading zeros: 00,000,0000,0101,0202,...
Lists of nonprimitive words over a subalphabet of {1...9}, like A213972, A213973, A213974, A239018, ... are given as intersection of this with the set of all words in that alphabet, e.g., A007931, A032810, A032917, A007932, ...


LINKS



MAPLE

F:= proc(d) local p, R, q;
R:= {seq(x*(10^d1)/9, x=1..9)};
for p in numtheory:factorset(d) minus {d} do
q:= d/p;
R:= R union {seq(x*(10^d1)/(10^q1), x=10^(q1)..10^q1)};
od:
sort(convert(R, list))
end proc:


PROG

(PARI) is_A239019(n)=fordiv(#n=digits(n), L, L<#n && n==concat(Col(vector(#n/L, i, 1)~*vecextract(n, 2^L1))~)&&return(1))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



