[seqfan] Multiply by the fantom digit

[Eric Angelini]

Hello SeqFans,
The idea is to multiply a(n) by the largest digit
not present in a(n) -- and iterate.
The iteration stops when the result shows all the
digits from 0 to 9, or from 1 to 9, or from 2 to 9.

Is there an integer that enters into an infinite
seq? I guess not.

I've tested below the starts for a(n) = 1, 2, 3 and 4.

Best,
É.
--------------------------------------------------

1 x 9 =
9 x 8 =
72 x 9 =
648 x 9 =
5832 x 9 =
52488 x 9 =
472392 x 8 =
3779136 x 8 =
30233088 x 9 =
272097792 x 8 =
2176782336 x 9 =
19591041024 x 8 =
156728328192 x 4 =
626913312768 x 5 =
3134566563840 x 9 =
28211099074560 x 3 =
84633297223680 x 5 =
423166486118400 x 9 =
3808498375065600 x 2 =
7616996750131200 x 8 =
60935974001049600 x 8 =
487487792008396800 x 5 =
243743896004198400000 x 5 =
1218719480020992000000 x 6 =
7312316880125952000000 x 4 =
29249267520503808000000 x 1 = stop

2 x 9 =
18 x 9 =
162 x 9 = 
1458 x 9 =
13122 x 9 =
118098 x 7 = 
826686 x 9 =
7440174 x 9 =
66961566 x 8 =
535692528 x 7 = 
3749847696 x 5 = 
18749238480 x 6 = 
112495430880 x 7 = 
787468016160 x 9 =
7087212145440 x 9 =
63784909308960 x 5 =
318924546544800 x 7 =
2232471825813600 x 9 =
20092246432322400 x 8 =
160737971458579200 x ... stop

3 x 9 =
27 x 9 = 
243 x 9 =
2187 x 9 =
19683 x 7 =
137781 x 9 =
1240029 x 8 =
9920232 x 8 =
79361856 x 4 =
317447424 x 9 =
2857026816 x 9 =
25713241344 x 9 =
231419172096 x 8 = 
1851353376768 x 9 =
16662180390912 x 7 =
116635262736384 x 9 =
1049717364627456 x 8 =
8397738917019648 x 5 = 
41988694585098240 x 7 =
293920862095687680 x 4 =
1175683448382750720 x 9 =
10581151035444756480 x 9 =
95230359319002808320 x 7 =
666612515233019658240 x 7 =
4666287606631137607680 x 9 =
41996588459680238469120 x 7 =
293976119217761669283840 x 5 = 
1469880596088808346419200 x 7 =
10289164172621658424934400 x ... = stop


4 x 9 =
36 x 9 =
324 x 9 = 
2916 x 8 =
23328 x 9 =
209952 x 8 =
1679616 x 8 =
13436928 x 7 =
94058496 x 7 =
658409472 x 3 =
1975228416 x 3 =
5925685248 x 7 =
41479796736 x 8 =
331838373888 x 9 =
2986545364992 x 7 =
20905817554944 x 6 =
125434905329664 x 8 =
1003479242637312 x 8 =
8027833941098496 x 5 =
40139169705492480 x ... = stop