A239019 - OEIS

%I #11 Jan 29 2019 15:13:06

%S 11,22,33,44,55,66,77,88,99,111,222,333,444,555,666,777,888,999,1010,

%T 1111,1212,1313,1414,1515,1616,1717,1818,1919,2020,2121,2222,2323,

%U 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

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

%C A word is primitive iff it is not a power, i.e., repetition, of a subword. The only non-primitive words with a prime number of letters (here: digits) are the repdigit numbers. Thus, the first nontrivial terms of this sequence are 1010,1212,...

%C This sequence does *not* contain all non-primitive words over the alphabet {0,...,9}, namely, it excludes those which would be numbers with leading zeros: 00,000,0000,0101,0202,...

%C Lists of non-primitive words over a sub-alphabet 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, ...

%H Robert Israel, <a href="/A239019/b239019.txt">Table of n, a(n) for n = 1..10000</a>

%p F:= proc(d) local p,R,q;

%p   R:= {seq(x*(10^d-1)/9, x=1..9)};

%p   for p in numtheory:-factorset(d) minus {d} do

%p     q:= d/p;

%p     R:= R union {seq(x*(10^d-1)/(10^q-1),x=10^(q-1)..10^q-1)};

%p   od:

%p   sort(convert(R,list))

%p end proc:

%p [seq(op(F(i)),i=2..4)]; # _Robert Israel_, Nov 14 2017

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

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Mar 08 2014