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A001151 Describe the previous term! (method A - initial term is 8).

%I A001151 #31 Sep 15 2024 22:09:35
%S A001151 8,18,1118,3118,132118,1113122118,311311222118,13211321322118,
%T A001151 1113122113121113222118,31131122211311123113322118,
%U A001151 132113213221133112132123222118,11131221131211132221232112111312111213322118,31131122211311123113321112131221123113111231121123222118
%N A001151 Describe the previous term! (method A - initial term is 8).
%C A001151 Method A = 'frequency' followed by 'digit'-indication.
%C A001151 a(n+1) - a(n) is divisible by 10^5 for n > 5. - _Altug Alkan_, Dec 04 2015
%D A001151 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 452-455.
%D A001151 I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 4.
%H A001151 T. D. Noe, <a href="/A001151/b001151.txt">Table of n, a(n) for n=1..20</a>
%H A001151 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 A001151 S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/cnwy/cnwy.html">Conway's Constant</a> [Broken link]
%H A001151 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 A001151 E.g. the term after 3118 is obtained by saying "one 3, two 1's, one 8", which gives 132118.
%p A001151 freq := proc(i,L)
%p A001151     local f,p ;
%p A001151     if i > nops(L) or i < 1 then
%p A001151         return 0 ;
%p A001151     end if;
%p A001151     f := 1 ;
%p A001151     for p from i to 2 by -1 do
%p A001151         if op(p,L) = op(p-1,L) then
%p A001151             f := f+1 ;
%p A001151         else
%p A001151             return f;
%p A001151         end if;
%p A001151     end do:
%p A001151     f ;
%p A001151 end proc:
%p A001151 read("transforms"):
%p A001151 rle := proc(n)
%p A001151     local inL,i,outL,f ;
%p A001151     inL := convert(n,base,10) ;
%p A001151     i := nops(inL) ;
%p A001151     outL := [] ;
%p A001151     while i>0 do
%p A001151         f := freq(i,inL) ;
%p A001151         if f = 0 then
%p A001151             break;
%p A001151         else
%p A001151             outL := [op(outL),f,op(i,inL)] ;
%p A001151             i := i-f ;
%p A001151         end if;
%p A001151     end do:
%p A001151     digcatL(outL) ;
%p A001151 end proc:
%p A001151 A001151 := proc(n)
%p A001151     option remember ;
%p A001151     if n = 1 then
%p A001151         8;
%p A001151     else
%p A001151         rle(procname(n-1)) ;
%p A001151     end if;
%p A001151 end proc:
%p A001151 seq(A001151(n),n=1..10) ; # _R. J. Mathar_, Feb 11 2021
%t A001151 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 A001151 Cf. A001155, A005150, A006751, A006715, A001140, A001141, A001143, A001145, A001154.
%K A001151 nonn,base,easy,nice
%O A001151 1,1
%A A001151 _N. J. A. Sloane_