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A239134
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Smallest k such that n^k contains k as a substring in its decimal representation.
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1
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1, 6, 7, 6, 2, 6, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 4, 2, 3, 2, 4, 2, 4, 3, 7, 1, 2, 3, 3, 2, 2, 3, 5, 2, 6, 1, 8, 4, 4, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 4, 2, 4, 3, 6, 1, 3, 5, 6, 2, 4, 3, 2, 3, 3, 1, 3, 2, 6, 2, 3, 2, 6, 2, 4, 1, 2, 4, 4
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OFFSET
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1,2
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COMMENTS
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Is it very likely a(n) < 10 for all n (even stronger, a(n) < 9 for all n).
Is it also very likely a(n) = {1,2,3} for sufficiently large n.
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LINKS
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FORMULA
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EXAMPLE
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5^1 = 5 does not contain a 1 but 5^2 = 25 does contain a 2 so a(5) = 2.
7^1 = 7 does not contain a 1, 7^2 = 49 does not contain a 2, but 7^3 = 343 does contain a 3 so a(7) = 3.
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MATHEMATICA
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a[n_] := Block[{k=1}, While[{} == StringPosition[ ToString[n^k], ToString[k]], k++]; k]; Array[a, 84] (* Giovanni Resta, Mar 11 2014 *)
sk[n_]:=Module[{k=1}, While[SequenceCount[IntegerDigits[n^k], IntegerDigits[k]] == 0, k++]; k]; Array[sk, 90] (* Harvey P. Dale, May 12 2022 *)
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PROG
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(Python)
def Sub(x):
..for n in range(10**3):
....if str(x**n).find(str(n)) > -1:
......return n
x = 1
while x < 10**3:
..print(Sub(x))
..x += 1
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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