# [seqfan] Re: help needed with sequences related to Kaprekar map

zak seidov zakseidov at yahoo.com
Wed Aug 19 21:56:33 CEST 2009

```Also,
a(7) = 420876 (as in A151959 )
a(8) = 7509843 (not upper limit, but exact value)

Zak

--- On Wed, 8/19/09, zak seidov <zakseidov at yahoo.com> wrote:

> From: zak seidov <zakseidov at yahoo.com>
> Subject: Re: [seqfan]  help needed with sequences related to Kaprekar map
> To: njas at research.att.com
> Cc: seqfan at seqfan.eu
> Date: Wednesday, August 19, 2009, 2:45 PM
> Neil,
> I confirm that, in A151959, a(3) = 64308654
> (no smaller number with cycle of length 3).
> I used brute force with Mathematica.
> Zak
>
>
>
> --- On Wed, 8/19/09, N. J. A. Sloane <njas at research.att.com>
> wrote:
>
> > From: N. J. A. Sloane <njas at research.att.com>
> > Subject: [seqfan]  help needed with sequences
> related to Kaprekar map
> > To: seqfan at seqfan.eu
> > Cc: njas at research.att.com
> > Date: Wednesday, August 19, 2009, 1:19 PM
> > Dear Sequence Fans,  Now that
> > the OEIS is "on vacation" I have
> > time to read the newspaper.  Yesterday's New York
> > Times (Science Section,
> > Aug 18 2009, last page) has three sequences as
> puzzles. Two
> > of
> > them were in the OEIS, the third was not (it is now
> > A151946).
> >
> > The rule for the third sequence is the Kaprekar map,
> see
> > A151949, given by
> >
> > n -> K(n) := (n with digits sorted into descending
> > order) - (n with digits sorted into ascending order)
> >
> > E.g. K(102) = 210 - (0)12 = 210 - 12 = 198.
> >
> > With help from Klaus Brockhaus and Harvey Dale, I
> have
> > added many new sequences
> > related to this map, and there is also an Index
> > entry.  The sequences related to
> > this map are presently:
> >
> > A151949*, A099009*, A099010, A069746, A090429,
> A132155,
> > A160761, A151946, A151947, A151950, A056965, A151951,
> > A151955, A151956, A151957, A151958, A151959, A151962,
> > A151963, A151964, A151965, A151966
> >
> > (Klaus's A099009 gives the fixed points)
> >
> > I am writing to ask the sequence fans for help in
> extending
> > these sequences - many
> > of them need more terms.
> >
> > The most important outstanding question concerns the
> > smallest cycle of length 3
> > - is it   64308654 -> 83208762 ->
> > 86526432 -> 64308654 ...  or is there a smaller
> > example?
> >
> > In other words, the third term of the following entry
> needs
> > to be confirmed or corrected!
> >
> > %I A151959
> > %S A151959 0,53955,64308654,62964
> > %N A151959 Consider the Kaprekar map x->K(x)
> described
> > in A151949. Sequence gives the smallest number that
> belongs
> > to a cycle of length n under repeated iteration of
> this map,
> > or -1 if there is no cycle of length n.
> > %C A151959 The term a(3) = 64308654 is only a
> conjecture,
> > and needs to be confirmed.
> > %C A151959 No cycles of lengths 5 0r 6 are presently
> > known.
> > %C A151959 It is also known that a(7) = 420876 and
> a(8)
> > <= 7509843.
> > %C A151959 A099009 gives the fixed points and A099010
> gives
> > numbers in cycles of length > 1.
> > %H A151959 <a
> href="Sindx_K.html#Kaprekar_map">Index
> > entries for the Kaprekar map</a>
> > %e A151959 a(1) = 0: 0 -> 0.
> > %e A151959 a(2) = 53955: 53955 -> 59994 ->
> 53955
> > -> ...
> > %e A151959 a(3) = 64308654?: 64308654 -> 83208762
> ->
> > 86526432 -> 64308654 -> 83208762 -> ..., but
> there
> > is a possibilty that a smaller example exists.
> > %O A151959 0,2
> > %K A151959 nonn,more
> > %A A151959 K. Brockhaus
> (klaus-brockhaus(AT)t-online.de)
> > and N. J. A. Sloane (njas(AT)research.att.com), Aug 19
> 2009
> >
> > But many others need extending too.
> >
> > Neil
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
>

```