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A248018
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Least number k > 0 such that n^k contains n*R_n in its decimal representation, or 0 if no such k exists.
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0
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1, 43, 119, 96, 186, 1740, 6177, 8421, 104191, 0, 946417
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OFFSET
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1,2
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COMMENTS
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R_n is the repunit of length n, i.e., R_n = (10^n-1)/9, A002275.
a(10^n) = 0 for all n > 0. - Derek Orr, Sep 29 2014
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LINKS
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EXAMPLE
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a(2) = 43 because 2^43 = 8796093022208 has the string '22' in it and 43 is the smallest power of 2 that produces such a result.
a(3) = 119 because 3^119 = 599003433304810403471059943169868346577158542512617035467 contains the string '333', and 119 is the smallest power of 3 that gives us such a result.
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PROG
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(Python)
def a(n):
..s = str(n)
..p = len(s)
..if s.count('1') == 1 and s.count('0') == p - 1:
....return 0
..k = 1
..while not str(n**k).count(n*s):
....k += 1
..return k
n = 1
while n < 10:
..print(a(n), end=', ')
..n += 1
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CROSSREFS
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KEYWORD
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base,nonn,hard,more
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AUTHOR
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EXTENSIONS
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a(3) and a(5) corrected, a(6)-a(8) added by Derek Orr, Sep 29 2014
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STATUS
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approved
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