

A324309


Smallest number m such that m is not a multiple of 10 and m^n has two or more identical adjacent decimal digits.


1



11, 12, 11, 16, 6, 6, 6, 4, 4, 6, 3, 3, 4, 7, 7, 2, 6, 2, 2, 3, 4, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2
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OFFSET

1,1


COMMENTS

Least number m such that m is not a multiple of 10 and m^n is a term of A171901.
a(n) >= 2 and a(n) exists for all n > 0, since for sufficiently large k, floor(10^(k/n))^n = 99.... and has 2 adjacent digits 9.
Conjecture: a(n) = 2 for n > 126, i.e., 2^n has two or more identical adjacent decimal digits for n > 126.


LINKS



EXAMPLE

a(4) = 16 since 16^4 = 65535 has a double digit 5, where i^4 does not have a double digit for i < 16.


PROG

(Python)
m, k = 2, 2**n
while True:
s = str(k)
for i in range(1, len(s)):
if s[i] == s[i1]:
return m
m += 1
if m % 10 == 0:
m += 1
k = m**n


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



