This site is supported by donations to The OEIS Foundation.
User:Daniel Mondot/Multiplicative Persistence
Contents
Current work on multiplicative persistence
multiplicative persistence tree
The file File:Multiplicative Persistence Tree.txt gives the path of (almost) all numbers back to a single digit. Numbers that are not of the path of another number are not part of this table.
Also, because there are an infinite number of numbers that are part of a path, and lead to 0 in 1 step. Only the ones that have an ascendant also in this table are listed.
Number in this file are located according to these rules:
- 1st column: multiplicative persistence of 0
- 2nd column: multiplicative persistence of 1
- 3rd column: multiplicative persistence of 2
- 4th column: multiplicative persistence of 3
- 5th column: multiplicative persistence of 4
- 6th column: multiplicative persistence of 5
- 7th column: multiplicative persistence of 6
- 8th column: multiplicative persistence of 7
- 9th column: multiplicative persistence of 8
- 10th column: multiplicative persistence of 9
- 11th column: multiplicative persistence of 10
Applying the multiplicative persistence process , the product of the digits of a number p(n) is the first number that is located up and to the left of the original number.
For example, p(117649) is 1512, which is the first number found to the left and up from 117649.
| multiplicative persistence | ||||||||||||
| ending in | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 0 | 1 | 11962 | 330 | 82 | 24 | 8 | 7 | 5 | 2 | 2 | 0 | |
| 1 | 1 | 0 | ||||||||||
| 2 | 1 | 3 | 7 | 12 | 9 | 1 | 0 | |||||
| 3 | 1 | 0 | ||||||||||
| 4 | 1 | 1 | 2 | 4 | 1 | 0 | ||||||
| 5 | 1 | 1 | 3 | 4 | 3 | 0 | ||||||
| 6 | 1 | 3 | 7 | 18 | 36 | 14 | 4 | 1 | 0 | |||
| 7 | 1 | 0 | ||||||||||
| 8 | 1 | 5 | 13 | 19 | 11 | 2 | 0 | |||||
| 9 | 1 | 0 | ||||||||||
Please note that in A003001, A.H.M. Smeets has a similar table in the comment section. His numbers are incorrect, except for final digits 1,3,5,7 and 9.
From a comment A003001 by Benjamin Chaffin in 2016, there are no more numbers with multiplicative persistence >1, between 10^140 and 10^20000.
I have been running my own search up to 10^30000, and finally, after 85.6 days, the program finished and didn't find any more numbers.
Some sequences about Multiplicative Persistence
- Multiplicative persistence 1 to 9:
- sequence offset data Programs comment
- A046510: 1,1 10000 mma/pari/python some
- A046511: 1,1 10000 mma/python none
- A046512: 1,1 10000 mma/maple none
- A046513: 1,1 10000 mma/maple none
- A046514: 1,1 10000 maple none
- A046515: 1,1 10000 maple none
- A046516: 1,1 10000 maple none
- A046517: 1,1 10000 mma/maple none
- A046518: 1,1 10000 maple none
- A352531: 1,1 (10000) (done in C) none in progress
- A352532: 1,1 (10000) (done in C) none in progress
- Multiplicative persistence 1 to 9 and prime:
- sequence offset data Programs comments
- A046501: 1,1 10000 mma/pari/python some
- A046502: 1,1 10000 ----------- none
- A046503: 1,1 10000 mma/maple none
- A046504: 1,1 10000 mathematica none
- A046505: 1,1 10000 mathematica none
- A046506: 1,1 10000 maple none
- A046507: 1,1 10000 ----------- none
- A046508: 1,1 10000 mathematica none
- A046509: 1,1 10000 ----------- none
- multiplicative persistence 10 and 11 might be missing.
- Multiplicative persistence 1 through 10 and 7-smooth.
- sequence offset data Programs comments
- A350180: 1,1 20000 pari yes
- A350181: 1,1 11994 mms/python yes
- A350182: 1,1 387 ---------- yes
- A350183: 1,1 142 mma/python/pari yes
- A350184: 1,1 41 mma/python yes
- A350185: 1,1 12 mma/python yes
- A350186: 1,1 8 mathematica yes
- A350187: 1,1 5 ----------- yes
- A350188: Sequence was recycled for being too short. It was supposed to contain: 438939648, 231928233984
- A350189: Sequence was recycled for being too short. It was supposed to contain: 4996238671872, 937638166841712
