| \(x\) | Weak Goodstein Function | Goodstein Function |
|---|---|---|
| 0 | 2 | 2 |
| 1 | 3 | 3 |
| 2 | 5 | 5 |
| 3 | 7 | 7 |
| 4 | 23 | \(2^{2^{27}3+27}3-1\approx10^{10^{8.0835}}\) |
| 5 | 63 | \(2^{...+2^{2^6+6}+2^6+6}\approx2\uparrow\uparrow\uparrow4\) |
| 6 | 383 | \(\approx2\uparrow\uparrow\uparrow\uparrow\uparrow6\) |
| 7 | 2047 | \(\approx2\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow8\) |
| 8 | \(2^{2^{27}3+27}3-1\approx10^{10^{8.0835}}\) | \(\approx2\uparrow^{2\uparrow^{2\uparrow\uparrow3}2\uparrow\uparrow3}2\uparrow^{2\uparrow\uparrow3}2\uparrow\uparrow3\) |
| 9 | \(\approx2\uparrow\uparrow4\) | \(\approx2\{\{1\}\}4\) |
| 10 | \(\approx2\uparrow\uparrow6\) | \(\approx2\{\{1\}\}6\) |
| 11 | \(\approx2\uparrow\uparrow8\) | \(\approx2\{\{1\}\}8\) |
| 12 | \(\approx2\uparrow\uparrow23\) | \(\approx2\{\{1\}\}10^{10^{8.0835}}\) |
| 13 | \(\approx2\uparrow\uparrow63\) | \(\approx2\{\{1\}\}2\uparrow\uparrow\uparrow4\) |
| 14 | \(\approx2\uparrow\uparrow383\) | \(\approx2\{\{1\}\}2\uparrow\uparrow\uparrow\uparrow\uparrow6\) |
| 15 | \(\approx2\uparrow\uparrow2047\) | \(\approx2\{\{1\}\}2\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow8\) |