Then each domino except the first only counts for one base 7 digit. 166144047 would go from 16:61:44:04 to 16:66:61:14:44:40:04.
That means that 6 or more decimal digits would then be more efficient than the same amount of dominos.
10^n >= 7^(n+1)
ln(10^n) >= ln(7^(n+1))
n*ln(10) >= (n+1)*ln(7)
n*ln(10) >= n*ln(7) + ln(7)
n*ln(10) - n*ln(7) >= ln(7)
n*( ln(10) - ln(7) ) >= ln(7)
n >= ln(7)/( ln(10) - ln(7) )
n >= 5.455696235812878344
n >= 6
$ perl -e'
printf "chars: %2d digits: %13.f %s dominoes: %11.f\n",
$_,
10**$_,
qw( < = > )[( 10**$_ <=> 7**($_+1) )+1],
7**($_+1),
for 1..12
'
chars: 1 digits: 10 < dominoes: 49
chars: 2 digits: 100 < dominoes: 343
chars: 3 digits: 1000 < dominoes: 2401
chars: 4 digits: 10000 < dominoes: 16807
chars: 5 digits: 100000 < dominoes: 117649
chars: 6 digits: 1000000 > dominoes: 823543
chars: 7 digits: 10000000 > dominoes: 5764801
chars: 8 digits: 100000000 > dominoes: 40353607
chars: 9 digits: 1000000000 > dominoes: 282475249
chars: 10 digits: 10000000000 > dominoes: 1977326743
chars: 11 digits: 100000000000 > dominoes: 13841287201
chars: 12 digits: 1000000000000 > dominoes: 96889010407
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