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A239018
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Non-primitive words on {1,2,3}.
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6
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11, 22, 33, 111, 222, 333, 1111, 1212, 1313, 2121, 2222, 2323, 3131, 3232, 3333, 11111, 22222, 33333, 111111, 112112, 113113, 121121, 121212, 122122, 123123, 131131, 131313, 132132, 133133, 211211, 212121, 212212, 213213, 221221, 222222, 223223, 231231, 232232, 232323, 233233, 311311, 312312, 313131, 313313
(list;
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history;
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OFFSET
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1,1
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COMMENTS
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A word is non-primitive if it is a nontrivial power (i.e., repetition) of a subword. Therefore, for a prime number of digits, only the repdigit numbers are primitive. For words with 6 letters, there is also 112^2,113^2,121^2,12^3,... where w^n means n concatenations of w.
Lyndon words on {1,2,3}, A102660, are the terms in A007932 which are primitive (i.e., in the complement A239017 of this sequence) and not larger than any of their rotation, i.e., in A239016.
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LINKS
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PROG
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(PARI) for(n=1, 7, p=vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [1, 3]), is_A239017(m=d*p)||print1(m", ")))
(Python)
from sympy import divisors
from itertools import product
def agentod(maxd):
for d in range(2, maxd+1):
divs, alld = divisors(d)[:-1], set()
for div in divs:
for t in product("123", repeat=div):
alld.add(int("".join(t*(d//div))))
yield from sorted(alld)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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