[seqfan] Re: Erased copies

Wed Oct 24 23:33:14 CEST 2018

First we throw out all digits that are repeated, then we thow out a leading
0 if it is followd by a nonzero digit.

so the answer is 2

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

On Wed, Oct 24, 2018 at 5:24 PM Allan Wechsler <acwacw at gmail.com> wrote:

> Under the "delete multiple digits" operation, does 10201 map to 20, or does
> it map to 2? Either answer makes sense, depending on the detailed
> definition of the map.
>
> On Wed, Oct 24, 2018 at 12:37 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > Correction: A320487 is
> >
> > a(0)= 1; thereafter a(n) is obtained by applying the "delete multiple
> > digits" map m -> A320485(m) to 2*a(n-1).
> > Best regards
> > Neil
> >
> >
> >
> >
> >
> > On Wed, Oct 24, 2018 at 12:28 PM Neil Sloane <njasloane at gmail.com>
> wrote:
> >
> > > Eric,  That is a lovely idea, one of your best!  I like it a lot.
> > >
> > > To start the ball rolling, I created A320485 for the basic operation
> > > applied
> > > just once to n itself, writing -1 if the result is the empty string.
> > >
> > > And I created A320486 for the basic operation applied
> > > just once to n itself, writing 0 if the result is the empty string. (I
> > > don't like it as much, but it
> > > has to be in the OEIS too).
> > >
> > > Then A320487 is the doubling sequence, starting with 1, which as you
> > > observed is periodic with period 28.
> > >
> > > Maybe you could send in some others , for example,
> > > - number of steps before the operation reaches a fixed point
> > > - the trebling sequence starting at 1
> > > - the finite "factorial" sequence in your email, which is
> > > 2 x 1    = 2
> > > 3 x 2    = 6
> > > 4 x 6    = 24
> > > 5 x 24   = 120
> > > 6 x 120  = 720
> > > 7 x 720  = (5040) = 54
> > > 8 x 54   = 432
> > > 9 x 432  = (3888) = 3
> > > 10 x 3   = 30
> > > 11 x 30  = 330
> > > End. Only 11 terms.
> > >
> > > -  the start a(1) = 2 generates 23 terms [last one
> > > being  23 x 198 = (4554) End]
> > > - the start a(1) = 3 produces only 12 terms [last one 12 x 407 = (4884)
> > > End].
> > >
> > > If you have time, please submit all these and more!
> > >
> > > Here is the wording I used for the doubling sequence A320487:
> > >
> > > a(0)= 1; thereafter a(n) is obtained by applying the "delete multiple
> > > digits" map m -> A320485(m) to a(n-1).
> > >
> > > At first I called this the Angelini map, but then I realized that you
> > > would not be able to use that name!
> > >
> > >
> > >
> > >
> > >
> > > On Wed, Oct 24, 2018 at 7:31 AM Éric Angelini <eric.angelini at skynet.be
> >
> > > wrote:
> > >
> > >> Hello SeqFan,
> > >> Take an integer and keep only its distinct digits in their
> > >> apparition order. Example:
> > >>
> > >> 1231 becomes 23
> > >> 1123 becomes 23
> > >> 11231 becomes 23
> > >> and
> > >> 11023 becomes 23 too (as we don't accept leading zeroes).
> > >> Note that 112323 disappears immediately.
> > >>
> > >> Now chose a function F, a starting term a(1) and iterate.
> > >>
> > >> Say, for instance, that the function F is "double" and a(1) is 19:
> > >>
> > >>
> > >>
> >
> 19,38,76,152,304,608,(1216),26,52,104,208,416,832,(1664),14,28,56,(112),2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,(65536),3,6,12,24,48,96,192,384,768,1536,3072,(6144),61,(122),1,2,
> > >> ... (loop).
> > >>
> > >> The "triple" function F starting with a(1) = 37 stops immediately,
> > >> of course (as 37 x 3 --> 111).
> > >>
> > >> The "square" function is interesting as some huge integers appear
> > >> – that sometimes collapse into a 2- or 3-digit integer. I didn't
> > >> explore thoroughly this domain (fixed points, loops, flights,
> > >> altitudes, etc.) -- only played a bit with the idea.
> > >>
> > >> A sequence I would like to see is the one dealing with the function
> > >> F = (n+1)*a(n) that would generate, for the smallest a(1), more
> > >> than 100 terms...
> > >>
> > >> For a(1) = 1, we have the sequence:
> > >>
> > >> 2 x 1    = 2
> > >> 3 x 2    = 6
> > >> 4 x 6    = 24
> > >> 5 x 24   = 120
> > >> 6 x 120  = 720
> > >> 7 x 720  = (5040) = 54
> > >> 8 x 54   = 432
> > >> 9 x 432  = (3888) = 3
> > >> 10 x 3   = 30
> > >> 11 x 30  = 330
> > >> End. Only 11 terms.
> > >>
> > >> If I'm not wrong, the start a(1) = 2 generates 23 terms [last one
> > >> being  23 x 198 = (4554) End] and the start a(1) = 3 produces only
> > >> 12 terms [last one 12 x 407 = (4884) End].
> > >> What would be the smallest a(1) generating 100 terms or more?
> > >>
> > >> P.-S.
> > >> A friend of mine thinks that no
> > >> integer < 10000000 generates
> > >> any 100-term sequence, according
> > >> to a program he wrote: the longest
> > >> sequence would have 78 terms
> > >> and the smallest generating-term
> > >> would be 19 128.
> > >>
> > >> Here is the 19 128 sequence [between
> > >> brackets are the terms that will
> > >> be "simplified"] :
> > >>
> > >> 19128 38256 [114768] 4768 19072 95360 572160 [4005120] 4512 [36096]
> 309
> > >> 2781 27810 [305910] 3591 43092 [560196] 5019 [70266] 702 [10530] 153
> > [2448]
> > >> 28 476 [8568] 56 1064 [21280] 180 3780 83160 [1912680] 92680 [2224320]
> > 430
> > >> [10750] 175 [4550] 40 [1080] 18 504 [14616] 4 120 3720 [119040] 94
> 3102
> > >> 105468 [3691380] 69180 [2490480] 298 [11026] 26 [988] 9 351 [14040] 1
> 41
> > >> [1722] 17 731 32164 [1447380] 17380 [799480] 7480 [351560] 3160
> [151680]
> > >> 5680 [278320] 7830 [391500] 3915 [199665] 15 780 [41340] 130 [7020] 72
> > 3960
> > >> [221760] 1760 [100320] 132 [7656] 75 [4425] 25 [1500] 15 915 56730
> > >> [3573990] 570 36480 [2371200] 371 [24486] 286 [19162] 962 [65416] 541
> > >> [37329] 729 [51030] 513 [36423] 642 [46224] 6 438 [32412] 341 [25575]
> 27
> > >> [2052] 5 385 [30030] 0 --> END.
> > >>
> > >> [Note: I've been away a long time from the SeqFan list -- and
> > >> if all this is old hat, please ignore this
> > >> and forgive me]
> > >> Best,
> > >> É.
> > >>
> > >>
> > >> à+
> > >> É.
> > >> Catapulté de mon aPhone
> > >>
> > >>
> > >> --
> > >> Seqfan Mailing list - http://list.seqfan.eu/
> > >>
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
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>