[seqfan] Re: Multiply by the fantom digit

[Bob Selcoe]

Hi Seqfans,

Nice, Lars and Eric!

It might be interesting to see the results if using smallest digit > 1 as 
the multiplier:

1*2 =
2*3 =
6*2 =
12 *3 =
36*2 =
72*3 =
216*3 =
...

I did a few smaller ones by hand and they all iterated to infinity.  Perhaps 
only a handful will terminate?

Best,
Bob Selcoe
PS - 53 terminates w/repeated 4,5,5 using this method.

--------------------------------------------------
From: "Lars Blomberg" <lars.blomberg at visit.se>
Sent: Wednesday, April 15, 2015 12:10 PM
To: "'Sequence Fanatics Discussion list'" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Multiply by the fantom digit

> Hello,
>
> Numbers that iterate to infinity with repeated multipliers 2,5 = 53, 68, 
> 82, 84, 85, 105, 124, 155, 158, 173, 202, 219, 238, 287, 303, 317, 335, 
> 349, 362, 367, 421, 424, 453, 465, 477, 481, 530, 533, 537, 542, 572, 612, 
> 615, 656, 663, 669, 671, 680, 687, 689, 703, 715, 737, 738, 756, 758, 765, 
> 797, 816, 820, 840, 842, 846, 850, 911, 919, 921, 931, 942, 945, 1007, 
> 1022, 1025, 1029, 1050, 1057, 1066, 1068, 1087, 1116, 1117, 1168, 1173, 
> 1175, 1212, 1216, 1236, 1240, 1241, 1297, 1302, 1308, 1326, 1349, 1387, 
> 1395, 1415, 1422, 1428, 1439, 1459, 1513, 1526, 1543, 1545, 1550, 1556, 
> 1557, 1562, 1580, 1581, 1583, 1588, 1616, 1618, 1634, 1646, 1659, 1730, 
> 1741, 1752, 1763, 1792, 1793, 1798, 1801, 1803, 1805, 1817, 1818, 1843, 
> 1876, 1894, 1896, 1914, 1922, 1923, 1933, 1934, 1939, 1945, 1947, 1958, 
> 1971, 1975, 1988, 2004, 2009, 2017, 2020, 2048, 2056, 2062, 2076, 2083, 
> 2108, 2114, 2123, 2127, 2142, 2158, 2159, 2190, 2201, 2211, 2267, 2298, 
> 2317, 2343, 2356, 2369, 2380, 2411, 2417, 2433, 2443, 2446, 2451, 2459, 
> 2491, 2505, 2522, 2526, 2536, 2551, 2571, 2583, ...
>
> Numbers with repeated multipliers 4,5,5 = 308, 1257, 1304, 2207, 2227, 
> 2553, 2772, 3009, 3080, 6757, 7021, 7073, 7484, 9307, 9355, 9533, 9662, 
> 9698, ...
>
> Numbers with repeated multipliers 8,5,5,5 = 385, 462, 529, 748, 935, 2273, 
> 2978, 3465, 3850, 4117, 4158, 4232, 4620, 4627, 4811, 5290, 5775, 6732, 
> 7480, 8309, 8529, 9051, 9076, 9350, 9448, 9523, 9559, 9714, ...
>
> /Lars
>
> -----Ursprungligt meddelande-----
> Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
> Skickat: den 15 april 2015 17:15
> Till: Sequence Fanatics Discussion list
> Kopia: alexandre.wajnberg at skynet.be
> Ämne: [seqfan] Multiply by the fantom digit
>
> 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
>
>
>
>
>
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