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Here is the raw python output for k up to 30, to avoid any gawk mishaps:
$ cat data2.txt
k 1 index 10
levels: 0
10 -> 69 0x45 7
k 2 index 100
levels: 1
100 -> 5764 0x1684 13
k 3 index 1000
levels: 2
1000 -> 526334 0x807FE 20
k 4 index 10000
levels: 3
10000 -> 50874761 0x3084989 26
k 5 index 100000
levels: 3
100000 -> 5028514748 0x12BB90BBC 33
k 6 index 1000000
levels: 3
1000000 -> 500918449417 0x74A110F509 39
k 7 index 10000000
levels: 3
10000000 -> 50029364025646 0x2D805E78992E 46
k 8 index 100000000
levels: 4
100000000 -> 5000934571821489 0x11C452D0B2C9B1 53
k 9 index 1000000000
levels: 4
1000000000 -> 500029664631299282 0x6F07654A9819CD2 59
k 10 index 10000000000
levels: 4
10000000000 -> 50000940106333921296 0x2B5E7061C419DA010 66
k 11 index 100000000000
levels: 4
100000000000 -> 5000029765607020319048 0x10F0D5A2486CA185148 73
k 12 index 1000000000000
levels: 4
1000000000000 -> 500000941936492050650505 0x69E11AF9D4B68A281589 79
k 13 index 10000000000000
levels: 4
10000000000000 -> 50000029798618763894670256 0x295BEB0BEDFC4C3D3B43B0 86
k 14 index 100000000000000
levels: 4
100000000000000 -> 5000000942529842698007077786 0x1027E762374D2B62E383E39A 93
k 15 index 1000000000000000
levels: 5
1000000000000000 -> 500000029809255627825531266625 0x64F9654B819C0B0427AA32641 99
k 16 index 10000000000000000
levels: 5
10000000000000000 -> 50000000942720152238624116795401 0x27716B7684EB9129B5951936809 106
k 17 index 100000000000000000
levels: 5
100000000000000000 -> 5000000029812655507343465281696595 0xF684DF6F6CF366E515963C973353 112
k 18 index 1000000000000000000
levels: 5
1000000000000000000 -> 500000000942780823112495107784753816 0x604BE740F05D25AE145E143A76C298 119
k 19 index 10000000000000000000
levels: 5
10000000000000000000 -> 50000000029813737262126730811322149673 0x259DA6548D98BAAC7E7EE6322EEC2B29 126
k 20 index 100000000000000000000
levels: 5
100000000000000000000 -> 5000000000942800098290022420982686040347 0xEB194F8ED94AC565124861C3B7D0C411B 132
k 21 index 1000000000000000000000
levels: 5
1000000000000000000000 -> 500000000029814080548392288266955229183571 0x5BD5E3139A066AAD8AF8E939162DA8B3E53 139
k 22 index 10000000000000000000000
levels: 5
10000000000000000000000 -> 50000000000942806209878293665994446398371544 0x23DF8CB3A1E2554E9C6BF863C38661F2936D8 146
k 23 index 100000000000000000000000
levels: 5
100000000000000000000000 -> 5000000000029814189323670710814676032031444555 0xE0352F62A75C24683091C00E99FD6AB95A4E4B 152
k 24 index 1000000000000000000000000
levels: 5
1000000000000000000000000 -> 500000000000942808145472258657037814775197247031 0x5794C68287D75EF3165412AE960B3F97A7C8A637 159
k 25 index 10000000000000000000000000
levels: 5
10000000000000000000000000 -> 50000000000029814223760934912839828327249688721190 0x22361D8AFCDFA146A21855C6F90DDAC4654C34F726 166
k 26 index 100000000000000000000000000
levels: 5
100000000000000000000000000 -> 5000000000000942808758091081952084125868709915711089 0xD5D238A4AC15D50E3D00380CE571F50DC9377ACD671 172
k 27 index 1000000000000000000000000000
levels: 5
1000000000000000000000000000 -> 500000000000029814234658067055252766458087914346630413 0x53861E20532CB00498751DF915A7CF79C1478C43FCD0D 179
k 28 index 10000000000000000000000000000
levels: 5
10000000000000000000000000000 -> 50000000000000942808951913512756782469229223199209677641 0x20A063C4A07BFE5299F1F53B301E47A1903967C6E1FE349 186
k 29 index 100000000000000000000000000000
levels: 5
100000000000000000000000000000 -> 5000000000000029814238105320163714566005337846445873165675 0xCBEA6F8CEB041179C7C69580FEB5120BE630BBDEAF99F56B 192
k 30 index 1000000000000000000000000000000
levels: 6
1000000000000000000000000000000 -> 500000000000000942809013222649956573426148951590151576716407 0x4FA793930BCD3B696B97D17F5ED30D4AD37D2F9880B58D8477 199