[seqfan] Multiply by the fantom digit

[Antti Karttunen]

On Wed, Apr 15, 2015 at 6:15 PM,  <seqfan-request at list.seqfan.eu> wrote:

>
> Message: 13
> Date: Wed, 15 Apr 2015 17:15:03 +0200
> From: Eric Angelini <Eric.Angelini at kntv.be>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Cc: "alexandre.wajnberg at skynet.be" <alexandre.wajnberg at skynet.be>
> Subject: [seqfan] Multiply by the fantom digit
> Message-ID:
>         <8B00BFBA136BAB43AD27F9EDC3758F03BD2846A630 at KNTVSRV01.kntv.local>
> Content-Type: text/plain; charset="iso-8859-1"
>
> 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 created three sequences A257079 - A257081 (in a draft queue now), where I use

A257079(n) the least nonzero digit in the factorial representation of
n (see https://oeis.org/A007623 )
to multiply n (= A257080(n)).

Nonzero so that there's a bit more change of avoiding stuck into a fixed point.

In range 0 - 3628800 (0 - 10!), all iterations of A257080 reach a
fixed point, with record lengths occurring at:

(starting value of n followed by the number of iterations to reach a
fixed point, i.e., a number with no 1 in its factorial base
representation):
awk -f records.awk < b257081_upto_10bang.txt
0 0
1 2
5 3
13 4
34 7
56 9
57 10
231 14
980 16
1094 17
1225 19
1607 23
7034 24
7552 25
14564 31
16049 39
291089 42
301892 45
345050 47
535093 54
1284547 55


Best regards,

Antti


>
> 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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