

A306494


Smallest number m such that n*3^m has 2 or more identical adjacent decimal digits.


2



11, 8, 10, 8, 11, 7, 9, 5, 9, 11, 0, 7, 2, 4, 10, 2, 4, 6, 7, 8, 8, 0, 5, 4, 2, 9, 8, 4, 6, 10, 4, 2, 0, 8, 6, 6, 1, 1, 1, 8, 3, 3, 3, 0, 9, 5, 5, 1, 2, 11, 3, 7, 2, 5, 0, 7, 6, 2, 1, 7, 6, 2, 7, 5, 3, 0, 6, 4, 4, 9, 7, 3, 5, 1, 1, 1, 0, 8, 2, 5, 7, 3, 3, 3, 1
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OFFSET

1,1


COMMENTS

a(n) is smallest m such that 3^m*n is in the sequence A171901 (or 1 if no such m exists).
0 <= a(n) <= 35 for all n > 0. This is proved by showing that for each 0 < n < 10^9, there is a number m <= 35 such that 3^m*n mod 10^9 has adjacent identical digits. If n > 0 and n == 0 mod 10^9, then clearly a(n) = 0.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000


FORMULA

a(A171901(n)) = 0.


EXAMPLE

a(1) = 11 since 3^11 = 177147 has 2 adjacent digits '7' and no smaller power of 3 has adjacent identical digits.
Record values:
a(1) = 11
a(241) = 12
a(2392) = 14
a(35698) = 15
a(267345) = 16
a(893521) = 17
a(29831625) = 18
a(3232453125) = 19


PROG

(Python)
def A306494(n):
m, k= 0, n
while True:
s = str(k)
for i in range(1, len(s)):
if s[i] == s[i1]:
return m
m += 1
k *= 3


CROSSREFS

Cf. A171901, A306305.
Sequence in context: A003567 A085688 A164059 * A068974 A244447 A206420
Adjacent sequences: A306491 A306492 A306493 * A306495 A306498 A306499


KEYWORD

nonn,base


AUTHOR

Chai Wah Wu, Feb 19 2019


STATUS

approved



