cp's OEIS Frontend

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.

The powers for the terms so far are 29, 3, 5, 5, 7, 7, 8, 11, 11, 11, 13, 12, 13, 18 and 15. A218170 is the opposing sequence with an extra copy of some digit. The 3-divisibility criterion precludes all digits appearing equally frequently. A217368 deals with the case not limited to primes.

Like A218169 but with an extra copy, rather than one less copy, of some digit. The exponents here are 2, 3, 5, 6, 7, 8, 8, 9, 10, 12, 11, 13, 15, 15, 16, 16 and 18. A217368 holds the sequence for powers of composites -- necessarily -- with equal counts of all digits.