The chart shows the (odd number) sequences generated by 6,631,675 (blue), 6,416,623 (pink) and 27 (red). 6,631,675 beats the previous record holder (6,416,623) by a factor of 12. The chart is a log (base 10) plot.
The route from a seed number (N) to it's ultimate destination at "1" will pass through a largest number, which I will call Max (N).
This page introduces the successive record holders for Max (N), and also the related values: Max(N)/N and log(Max(N))/log(N). We will only be dealing with odd numbers, If you were to recalculate these values including the event numbers then the actual Max(N) would be 3*Max(N)+1, which appears as "Even Max" in the table.
The following table shows the values of the three terms introduced above for the first few odd seeds, and highlights new records along the way.
The following table shows the values of the terms introduced above for the first few odd seeds, and highlights new records along the way.
| N | Max (N) | Max(N) / N | log (Max(N)) / log (N) | Even Max |
|---|---|---|---|---|
| 3 | 5 | 1.6667 | 1.4650 | 16 |
| 5 | 5 | 1.0000 | 1.0000 | 16 |
| 7 | 17 | 2.4286 | 1.4560 | 52 |
| 9 | 17 | 1.8889 | 1.2894 | 52 |
| 11 | 17 | 1.5455 | 1.1815 | 52 |
| 13 | 13 | 1.0000 | 1.0000 | 40 |
| 15 | 53 | 3.5333 | 1.4661 | 160 |
| 17 | 17 | 1.0000 | 1.0000 | 52 |
| 19 | 29 | 1.5263 | 1.1436 | 88 |
| 21 | 21 | 1.0000 | 1.0000 | 64 |
| 23 | 53 | 2.3043 | 1.2662 | 160 |
| 25 | 29 | 1.1600 | 1.0461 | 88 |
| 27 | 3077 | 113.9630 | 2.4369 | 9232 |
| 29 | 29 | 1.0000 | 1.0000 | 88 |
| 31 | 3077 | 99.2581 | 2.3389 | 9232 |
| 33 | 33 | 1.0000 | 1.0000 | 100 |
| 35 | 53 | 1.5143 | 1.1167 | 160 |
| 37 | 37 | 1.0000 | 1.0000 | 112 |
| 39 | 101 | 2.5897 | 1.2597 | 304 |
The next table extends this search up to seeds of about 100,000. Some quite large numbers are encountered along they way: The Max(n) record is broken quite frequently, and the Max(N)/N record is hanging on in there, but the log (Max(N)) / log (N) record set by 27 doesn't look like being broken. It looks like it might stay below 2, in which case Max(N) will always be less than N squared.
| N | Max (N) | Max(N) / N | log (Max(N)) / log (N) |
|---|---|---|---|
| 3 | 5 | 1.6667 | 1.4650 |
| 7 | 17 | 2.4286 | 1.4560 |
| 15 | 53 | 3.5333 | 1.4661 |
| 27 | 3,077 | 113.9630 | 2.4369 |
| 255 | 4,373 | 17.1490 | 1.5129 |
| 447 | 13,121 | 29.3535 | 1.5538 |
| 639 | 13,841 | 21.6604 | 1.4761 |
| 703 | 83,501 | 118.7781 | 1.7288 |
| 1,819 | 425,645 | 233.9995 | 1.7268 |
| 4,255 | 2,270,045 | 533.5006 | 1.7515 |
| 4,591 | 2,717,873 | 592.0002 | 1.7571 |
| 9,663 | 9,038,141 | 935.3349 | 1.7455 |
| 20,895 | 16,714,421 | 799.9244 | 1.6720 |
| 26,623 | 35,452,673 | 1,331.6558 | 1.7060 |
| 31,911 | 40,337,621 | 1,264.0663 | 1.6887 |
| 60,975 | 197,759,717 | 3,243.2918 | 1.7337 |
| 77,671 | 523,608,245 | 6,741.3609 | 1.7829 |
| 113,383 | 827,370,449 | 7,297.1296 | 1.7643 |
| 138,367 | 932,774,453 | 6,741.3072 | 1.7447 |
| 159,487 | 5,734,125,917 | 35,953.5630 | 1.8756 |
| 270,271 | 8,216,025,965 | 30,399.2140 | 1.8253 |
| 665,215 | 17,494,428,437 | 26,298.9085 | 1.7590 |
| 704,511 | 18,997,161,173 | 26,965.0313 | 1.7577 |
| 1,042,431 | 30,079,718,549 | 28,855.3569 | 1.7411 |
| 1,212,415 | 46,548,912,269 | 38,393.5470 | 1.7535 |
| 1,441,407 | 50,543,191,457 | 35,065.1769 | 1.7379 |
| 1,875,711 | 51,968,116,565 | 27,705.8228 | 1.7082 |
| 1,988,859 | 52,304,792,741 | 26,298.8944 | 1.7017 |
| 2,643,183 | 63,486,606,161 | 24,018.9976 | 1.6821 |
| 2,684,647 | 117,539,270,981 | 43,782.0209 | 1.7219 |
| 3,041,127 | 207,572,633,873 | 68,255.1679 | 1.7457 |
| 3,873,535 | 286,185,056,525 | 73,882.1404 | 1.7390 |
| 4,637,979 | 439,600,764,977 | 94,782.8278 | 1.7465 |
| 5,656,191 | 804,164,538,869 | 142,174.2192 | 1.7631 |
| 6,416,623 | 1,599,998,981,789 | 249,352.1876 | 1.7928 |
| 6,631,675 | 20,114,203,639,877 | 3,033,050.2686 | 1.9502 |
The chart shows the (odd number) sequences generated by 6,631,675 (blue), 6,416,623 (pink) and 27 (red). 6,631,675 beats the previous record holder (6,416,623) by a factor of 12. The chart is a log (base 10) plot.