A334686Start with n, and successively apply phi, phi, sigma', phi, phi, sigma', phi, ... until reaching either 0 or 1; a(n) is the number of steps needed (phi = A000010, sigma' = A001065); or a(n) = -1 if 0 or 1 is never reached.
0, 1, 2, 2, 3, 2, 3, 3, 3, 3, 5, 3, 5, 3, 5, 5, …
The first term appear at position 32.
…5358979323846264338327950288419716939937510582097…
…59408128481117450284102701938521105559644622948954…
…896091736371787214684409012249534301465495853710507…
…8960917363717872146844090122495343014654958537105079…
…48469793854226216871614001223782137797741312689772667…
…589024407549618407932214012232316540916975720858922578…
…5890244075496184079322140122323165409169757208589225789…
…40327986582329455741882801223233335381217602113868918786…
…403279865823294557418828012232333353812176021138689187867…
…4032798658232945574188280122323333538121760211386891878673…
…40327986582329455741882801223233335381217602113868918786734…
…403279865823294557418828012232333353812176021138689187867345…
| terms | string | first position | occurrences |
|---|---|---|---|
| 1 | 0 | 32 | 99,993,942 |
| 2 | 01 | 167 | 9,998,250 |
| 3 | 012 | 659 | 999,856 |
| 4 | 0122 | 659 | 100,223 |
| 5 | 01223 | 87,385 | 10,193 |
| 6 | 012232 | 3,392,133 | 998 |
| 7 | 0122323 | 3,392,133 | 102 |
| 8 | 01223233 | 46,821,206 | 14 |
| 9 | 012232333 | 46,821,206 | 2 |
| 10 | 0122323333 | 46,821,206 | 1 |
| 11 | 01223233335 | 46,821,206 | 1 |
| 12 | 012232333353 | 46,821,206 | 1 |
Searched the first 1,000,000,000 digits. Strings longer than 12 digits are not indexed.