› $a = 10
10
› sprintf '%.f', $a += (100-10)/7
23
› sprintf '%.f', $a += (100-10)/7
36
› sprintf '%.f', $a += (100-10)/7
49
› sprintf '%.f', $a += (100-10)/7
61
› sprintf '%.f', $a += (100-10)/7
74
› sprintf '%.f', $a += (100-10)/7
87
› sprintf '%.f', $a += (100-10)/7
100

› $a = 10
10
› sprintf '%.f', $a += (100-10)/3
40
› sprintf '%.f', $a += (100-10)/3
70
› sprintf '%.f', $a += (100-10)/3
100

##</code><code>##

› $a = 10
10
› sprintf '%.f', $a *= 10**(1/7)
14
› sprintf '%.f', $a *= 10**(1/7)
19
› sprintf '%.f', $a *= 10**(1/7)
27
› sprintf '%.f', $a *= 10**(1/7)
37
› sprintf '%.f', $a *= 10**(1/7)
52
› sprintf '%.f', $a *= 10**(1/7)
72
› sprintf '%.f', $a *= 10**(1/7)
100

› $a = 10
10
› sprintf '%.f', $a *= 10**(1/3)
22
› sprintf '%.f', $a *= 10**(1/3)
46
› sprintf '%.f', $a *= 10**(1/3)
100

##</code><code>##

# playground
my ($start, $end) = (10, 100);  # try: (35, 7400)
for my $step (1..20) {
    printf 'step %2d:', $step;
    my $i = $start;
    for (1..$step+1) {
        printf ' %.f', $i;
        $i *= ($end/$start)**(1/$step);
    }
    print "\n";
}
__END__
step  1: 10 100
step  2: 10 32 100
step  3: 10 22 46 100
step  4: 10 18 32 56 100
step  5: 10 16 25 40 63 100
step  6: 10 15 22 32 46 68 100
step  7: 10 14 19 27 37 52 72 100
step  8: 10 13 18 24 32 42 56 75 100
step  9: 10 13 17 22 28 36 46 60 77 100
step 10: 10 13 16 20 25 32 40 50 63 79 100
step 11: 10 12 15 19 23 28 35 43 53 66 81 100
step 12: 10 12 15 18 22 26 32 38 46 56 68 83 100
step 13: 10 12 14 17 20 24 29 35 41 49 59 70 84 100
step 14: 10 12 14 16 19 23 27 32 37 44 52 61 72 85 100
step 15: 10 12 14 16 18 22 25 29 34 40 46 54 63 74 86 100
step 16: 10 12 13 15 18 21 24 27 32 37 42 49 56 65 75 87 100
step 17: 10 11 13 15 17 20 23 26 30 34 39 44 51 58 67 76 87 100
step 18: 10 11 13 15 17 19 22 24 28 32 36 41 46 53 60 68 77 88 100
step 19: 10 11 13 14 16 18 21 23 26 30 34 38 43 48 55 62 70 78 89 100
step 20: 10 11 13 14 16 18 20 22 25 28 32 35 40 45 50 56 63 71 79 89 100