| Index/Indices | Element(s) | Number of Elements resp. Indices | Pair of Indices to form First Element | Left Summand of First Element | Right Summand of First Element | First Element is generated by Smallstep No | Number of 1-bits in binary representation |
| 0 | 1 | 1 | - | 1 | |||
| 1 | 2 | 1 | (0,0) | \(1\) | \(1\) | - | 1 |
| 2,...,5 | 3,...,24 | 4 | (1,0) | \(2\) | \(1\) | 1 | 2 |
| 6,...,10 | \(2 (2^4-1),...,2^5 (2^4-1)\) | 5 | (5,3) | \(24\) | \(6\) | 2 | 4 |
| 11 | \(2^9-29\) | 1 | (10,2) | \(2^5 (2^4 - 1)\) | \(3\) | 3 | 6 |
| 12,...,15 | \(2^{10}-61,...,2^3(2^{10}-61)\) | 4 | (11,10)\(^*\) | \(2^9-29\) | \(2^5 (2^4-1)\) | - | 6 |
| 16 | \(2^{13}-5\) | 1 | (15,11) | \(2^3(2^{10}-61)\) | \(2^9-29\) | 4 | 12 |
| 17 | \(2^{13}-3\) | 1 | (16,1)\(^*\) | \(2^{13}-5\) | \(2\) | 5 | 12 |
| 18,...,28 | \(2^3 (2^{11}-1),...,2^{13} (2^{11}-1)\) | 11 | (17,16)\(^*\) | \(2^{13}-3\) | \(2^{13}-5\) | - | 11 |
| 29 | \(2^{24}-3\) | 1 | (28,17) | \(2^{13} (2^{11}-1)\) | \(2^{13}-3\) | 6 | 23 |
| 30 | \(2^{24}-1\) | 1 | (29,1) | \(2^{24}-3\) | \(2\) | 7 | 24 |
| 31,...,53 | \(2^2 (2^{23}-1),...,2^{24} (2^{23}-1)\) | 23 | (30,29)\(^*\) | \(2^{24}-1\) | \(2^{24}-3\) | - | 23 |
| 54,...,78 | \(2^{47}-1,...,2^{24} (2^{47}-1)\) | 25 | (53,30) | \(2^{24} (2^{23}-1)\) | \(2^{24}-1\) | 8 | 47 |
| 79,...,126 | \(2^{71}-1,...,2^{47} (2^{71}-1)\) | 48 | (78,30) | \(2^{24} (2^{47}-1)\) | \(2^{24}-1\) | 9 | 71 |
| 127,...,245 | \(2^{118}-1,...,2^{118} (2^{118}-1)\) | 119 | (126,54) | \(2^{47} (2^{71}-1)\) | \(2^{47}-1\) | 10 | 118 |
| 246,...,482 | \(2^{236}-1,...,2^{236} (2^{236}-1)\) | 237 | (245,127) | \(2^{118} (2^{118}-1)\) | \(2^{118}-1\) | 11 | 236 |
| 483,...,955 | \(2^{472}-1,...,2^{472} (2^{472}-1)\) | 473 | (482,246) | \(2^{236} (2^{236}-1)\) | \(2^{236}-1\) | 12 | 472 |
| 956,...,1900 | \(2^{944}-1,...,2^{944} (2^{944}-1)\) | 945 | (955,483) | \(2^{472} (2^{472}-1)\) | \(2^{472}-1\) | 13 | 944 |
| 1901,...,3789 | \(2^{1888}-1,...,2^{1888} (2^{1888}-1)\) | 1889 | (1900,956) | \(2^{944} (2^{944}-1)\) | \(2^{944}-1\) | 14 | 1888 |
| 3790,...,7566 | \(2^{3776}-1,...,2^{3776} (2^{3776}-1)\) | 3777 | (3789,1901) | \(2^{1888} (2^{1888}-1)\) | \(2^{1888}-1\) | 15 | 3776 |
| 7567,...,7581 | \(2^{7552}-1,...,2^{14} (2^{7552}-1)\) | 15 | (7566,3790) | \(2^{3776} (2^{3776}-1)\) | \(2^{3776}-1\) | 16 | 7552 |
| 7582,...,15145 | \(2^3 (2^{7563}-1),...,2^{7566} (2^{7563}-1)\) | 7564 | (7581,18) | \(2^{14} (2^{7552}-1)\) | \(2^3 (2^{11}-1)\) | 17 | 7563 |
| 15146,...,30272 | \(2^3 (2^{15126}-1),...,2^{15129} (2^{15126}-1)\) | 15127 | (15145,7582) | \(2^{7566} (2^{7563}-1)\) | \(2^3 (2^{7563}-1)\) | 18 | 15126 |
| 30273,...,60525 | \(2^3 (2^{30252}-1),...,2^{30255} (2^{30252}-1)\) | 30253 | (30272,15146) | \(2^{15129} (2^{15126}-1)\) | \(2^3 (2^{15126}-1)\) | 19 | 30252 |
| 60526,...,121030 | \(2^3 (2^{60504}-1),...,2^{60507} (2^{60504}-1)\) | 60505 | (60525,30273) | \(2^{30255} (2^{30252}-1)\) | \(2^3 (2^{30252}-1)\) | 20 | 60504 |
| 121031,...,242039 | \(2^3 (2^{121008}-1),...,2^{121011} (2^{121008}-1)\) | 121009 | (121030,60526) | \(2^{60507} (2^{60504}-1)\) | \(2^3 (2^{60504}-1)\) | 21 | 121008 |
| 242040,...,484056 | \(2^3 (2^{242016}-1),...,2^{242019} (2^{242016}-1)\) | 242017 | (242039,121031) | \(2^{121011} (2^{121008}-1)\) | \(2^3 (2^{121008}-1)\) | 22 | 242016 |
| 484057,...,968089 | \(2^3 (2^{484032}-1),...,2^{484035} (2^{484032}-1)\) | 484033 | (484056,242040) | \(2^{242019} (2^{242016}-1)\) | \(2^3 (2^{242016}-1)\) | 23 | 484032 |
| 968090,...,1936154 | \(2^3 (2^{968064}-1),...,2^{968067} (2^{968064}-1)\) | 968065 | (968089,484057) | \(2^{484035} (2^{484032}-1)\) | \(2^3 (2^{484032}-1)\) | 24 | 968064 |
| 1936155,...,3872283 | \(2^3(2^{1936128}-1),...,2^{1936131} (2^{1936128}-1)\) | 1936129 | (1936154,968090) | \(2^{968067} (2^{968064}-1)\) | \(2^3 (2^{968064}-1)\) | 25 | 1936128 |
| 3872284,...,7744540 | \(2^3(2^{3872256}-1),...,2^{3872259}(2^{3872256}-1)\) | 3872257 | (3872283,1936155) | \(2^{1936131} (2^{1936128}-1)\) | \(2^3 (2^{1936128}-1)\) | 26 | 3872256 |
| 7744541,...,15489053 | \(2^3(2^{7744512}-1),...,2^{7744515}(2^{7744512}-1)\) | 7744513 | (7744540,3872284) | \(2^{3872259} (2^{3872256}-1)\) | \(2^3 (2^{3872256}-1)\) | 27 | 7744512 |
| 15489054,...,30978078 | \(2^3(2^{15489024}-1),...,2^{15489027}(2^{15489024}-1)\) | 15489025 | (15489053,7744541) | \(2^{7744515} (2^{7744512}-1)\) | \(2^3 (2^{7744512}-1)\) | 28 | 15489024 |
| 30978079,...,30978147 | \(2^3(2^{30978048}-1),...,2^{71}(2^{30978048}-1)\) | 69 | (30978078,15489054) | \(2^{15489027} (2^{15489024}-1)\) | \(2^3 (2^{15489024}-1)\) | 29 | 30978048 |
| 30978148 | \(2^{30978119}-1\) | 1 | (30978147,79) | \(2^{71} (2^{30978048}-1)\) | \(2^{71}-1\) | 30 | 30978119 |
Thus we have \(l(2^{30978119}-1)\le 30978148<l(30978119)+30978119-1=31+30978119-1=30978149\).
This counter-example is a star-chain for 230978119-1 which was constructed by Neill Clift on 1st July 2024.