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There is a bug in gawk 4.1.4, which was used to generate the table from >>23, which causes the second column, that of R values, to be wrong starting with k=9. You can see that the value of R(10^10) stated in >>18, which is the correct value from raw python output, differs from the value from >>23 for k=10. The values stated from raw python output are correct, only the R column of >>23 is wrong starting with k=9. Here is the raw python output with the correct values:
$ cat data.txt
groups: 4 index: 1
10: 69 0x0000000000000045
groups: 12 index: 3
100: 5764 0x0000000000001684
groups: 41 index: 7
1000: 526334 0x00000000000807FE
groups: 133 index: 13
10000: 50874761 0x0000000003084989
groups: 431 index: 25
100000: 5028514748 0x000000012BB90BBC
groups: 1384 index: 47
1000000: 500918449417 0x00000074A110F509
groups: 4416 index: 87
10000000: 50029364025646 0x00002D805E78992E
groups: 14039 index: 157
100000000: 5000934571821489 0x0011C452D0B2C9B1
groups: 44534 index: 285
1000000000: 500029664631299282 0x06F07654A9819CD2
groups: 141082 index: 512
10000000000: 50000940106333921296 0x2B5E7061C419DA010
groups: 446604 index: 920
100000000000: 5000029765607020319048 0x10F0D5A2486CA185148
groups: 1413120 index: 1647
1000000000000: 500000941936492050650505 0x69E11AF9D4B68A281589
groups: 4470180 index: 2944
10000000000000: 50000029798618763894670256 0x295BEB0BEDFC4C3D3B43B0
groups: 14138641 index: 5255
100000000000000: 5000000942529842698007077786 0x1027E762374D2B62E383E39A
groups: 44715123 index: 9372
1000000000000000: 500000029809255627825531266625 0x64F9654B819C0B0427AA32641Here is a diff between the values from the raw python output and the R column of >>23:
$ diff <(grep -e ' 0x' data.txt | cut -d ' ' -f 2) <(sed -r -e 's/^ *[0-9]+ +([0-9]+) +.+$/\1/' epsilon.txt)
9,15c9,15
< 500029664631299282
< 50000940106333921296
< 5000029765607020319048
< 500000941936492050650505
< 50000029798618763894670256
< 5000000942529842698007077786
< 500000029809255627825531266625
---
> 500029664631299264
> 50000940106333921280
> 5000029765607020822528
> 500000941936492081577984
> 50000029798618762867376128
> 5000000942529842273283211264
> 500000029809255645132191956992