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
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$ 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
[download]