A001151 - OEIS

%I #31 Sep 15 2024 22:09:35

%S 8,18,1118,3118,132118,1113122118,311311222118,13211321322118,

%T 1113122113121113222118,31131122211311123113322118,

%U 132113213221133112132123222118,11131221131211132221232112111312111213322118,31131122211311123113321112131221123113111231121123222118

%N Describe the previous term! (method A - initial term is 8).

%C Method A = 'frequency' followed by 'digit'-indication.

%C a(n+1) - a(n) is divisible by 10^5 for n > 5. - _Altug Alkan_, Dec 04 2015

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.

%D I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.

%H T. D. Noe, <a href="/A001151/b001151.txt">Table of n, a(n) for n=1..20</a>

%H J. H. Conway, <a href="http://dx.doi.org/10.1007/978-1-4612-4808-8_53">The weird and wonderful chemistry of audioactive decay</a>, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 173-188.

%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/cnwy/cnwy.html">Conway's Constant</a> [Broken link]

%H S. R. Finch, <a href="http://web.archive.org/web/20010207194413 /http://www.mathsoft.com/asolve/constant/cnwy/cnwy.html">Conway's Constant</a> [From the Wayback Machine]

%e E.g. the term after 3118 is obtained by saying "one 3, two 1's, one 8", which gives 132118.

%p freq := proc(i,L)

%p     local f,p ;

%p     if i > nops(L) or i < 1 then

%p         return 0 ;

%p     end if;

%p     f := 1 ;

%p     for p from i to 2 by -1 do

%p         if op(p,L) = op(p-1,L) then

%p             f := f+1 ;

%p         else

%p             return f;

%p         end if;

%p     end do:

%p     f ;

%p end proc:

%p read("transforms"):

%p rle := proc(n)

%p     local inL,i,outL,f ;

%p     inL := convert(n,base,10) ;

%p     i := nops(inL) ;

%p     outL := [] ;

%p     while i>0 do

%p         f := freq(i,inL) ;

%p         if f = 0 then

%p             break;

%p         else

%p             outL := [op(outL),f,op(i,inL)] ;

%p             i := i-f ;

%p         end if;

%p     end do:

%p     digcatL(outL) ;

%p end proc:

%p A001151 := proc(n)

%p     option remember ;

%p     if n = 1 then

%p         8;

%p     else

%p         rle(procname(n-1)) ;

%p     end if;

%p end proc:

%p seq(A001151(n),n=1..10) ; # _R. J. Mathar_, Feb 11 2021

%t RunLengthEncode[x_List] := (Through[{First, Length}[ #1]] &) /@ Split[x]; LookAndSay[n_, d_: 1] := NestList[Flatten[Reverse /@ RunLengthEncode[ # ]] &, {d}, n - 1]; F[n_] := LookAndSay[n, 8][[n]]; Table[FromDigits[F[n]], {n, 1, 11}] (* _Zerinvary Lajos_, Jul 08 2009 *)

%Y Cf. A001155, A005150, A006751, A006715, A001140, A001141, A001143, A001145, A001154.

%K nonn,base,easy,nice

%O 1,1

%A _N. J. A. Sloane_