

A239019


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


4



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

Robert Israel, Table of n, a(n) for n = 1..10000


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:
[seq(op(F(i)), i=2..4)]; # Robert Israel, Nov 14 2017


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

Sequence in context: A299792 A115853 A050785 * A033023 A014181 A302438
Adjacent sequences: A239016 A239017 A239018 * A239020 A239021 A239022


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Mar 08 2014


STATUS

approved



