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A217378 Exponents for the terms in A217368: least number which taken to the a(n)-th power has exactly n copies of each decimal digit. 2
2, 4, 5, 7, 9, 9, 9, 11, 12, 13, 13, 15, 15, 16, 16, 18, 18, 20, 23, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

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.

CROSSREFS

Cf. A217368 and references therein.

Sequence in context: A103118 A262969 A158029 * A140204 A084577 A202129

Adjacent sequences:  A217375 A217376 A217377 * A217379 A217380 A217381

KEYWORD

nonn,base

AUTHOR

James G. Merickel, Oct 01 2012

EXTENSIONS

Edited by M. F. Hasler, Oct 05 2012

a(13) and a(14) added by James G. Merickel, Oct 06 2012 and Oct 08 2012

a(15)-a(19) added by James G. Merickel, Oct 19 2012

a(20) added by James G. Merickel, Nov 28 2012

STATUS

approved

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)