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A217378
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Exponents for the terms in A217368: least number which taken to the a(n)-th power has exactly n copies of each decimal digit.
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2
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2, 4, 5, 7, 9, 9, 9, 11, 12, 13, 13, 15, 15, 16, 16, 18, 18, 20, 23, 21
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OFFSET
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1,1
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COMMENTS
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This sequence gives the exponents a(n) such that A217368(n)^a(n) has n copies of each digit 0-9.
In the limit of large k, the probability of a uniformly selected 10k-digit number having k copies of each base-10 digit is C*k^(-4.5), where C is approximately 8.09451*10^(-4) (by the use of Stirling's approximation to the factorial function applied to the multinomial corresponding to the number of such 10k-digit numbers divided by the total number of 10k-digit numbers). Also, the number of n-th powers of this length is very nearly equal to (1-10^(-1/n))*10^(10k/n) as long as n is not too large. That is, the former probability is reciprocal polynomial in k, while the number of n-th powers for a given n is exponential in k as long as k is large enough. Then, under the assumption that the digits of powers are randomly distributed, this sequence will increase without bound. A217378(n+1) < A217378(n) for the first time for n=19.
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LINKS
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EXAMPLE
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A217368(3) = 643905 raised to the 5th power has exactly 3 copies of each digit in its decimal representation, and no number smaller than 643905 has a power of the same nature. Therefore a(3)=5.
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CROSSREFS
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Cf. A217368 and references therein.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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