%I A100002
%S A100002 1,2,1,2,3,3,1,2,4,4,3,4,1,2,5,5,3,5,1,2,4,5,3,4,6,6,1,2,6,3,7,7,6,4,7,
%T A100002 7,5,6,1,2,5,3,8,8,7,4,8,8,1,2,6,7,3,6,5,8,4,8,5,6,9,9,1,2,9,3,10,10,9,
%U A100002 4,10,10,7,8,9,5,7,10,1,2,9,7,3,4,9,6,11,11,10,11
%N A100002 Start with a sequence of 1's, then replace every other 1 by a 2; then 
               replace every third of the remaining 1's by a 3 and every third of 
               the remaining 2's by a 3; then replace ever fourth remaining 1, 2 
               or 3 by a 4; and so on. The limiting sequence is shown here.
%C A100002 The position of the 1's is given by A000960. - T. D. Noe, Oct 26 2004
%H A100002 T. D. Noe, <a href="b100002.txt">Table of n, a(n) for n=1..10000</a>
%H A100002 T. D. Noe, <a href="a098119.gif">Plot of first 5000 terms</a>
%H A100002 A <a href="http://www.google.com/groups?selm=clhfm9%243eu%241%40news.ks.uiuc.edu">
               post</a> on sci.math.research newsgroup.
%F A100002 a(1, j)=1 for all j>=1; a(n, j)=a(n-1, j) except when #{i<=j s.t. a(n-1, 
               i)=a(n-1, j)} is multiple of n, in which case a(n, j)=n; a(j) is 
               the limit of the (stationary) a(n, j) when n tends to infinity.
%F A100002 It appears that that the maximal value among the first n terms grows 
               like sqrt(4n/3).
%F A100002 Note that the first occurrence of n is bounded by A000960; that is, A100287(n) 
               <= A000960(n), with equality only for n=1. - T. D. Noe (noe(AT)sspectra.com), 
               Nov 12 2004
%e A100002 Here are the first 6 stages in the construction:
%e A100002 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1...
%e A100002 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2...
%e A100002 1 2 1 2 3 3 1 2 1 2 3 3 1 2 1 2 3 3 1 2 1 2 3 3 1 2 1 2 3 3...
%e A100002 1 2 1 2 3 3 1 2 4 4 3 4 1 2 1 2 3 3 1 2 4 4 3 4 1 2 1 2 3 3...
%e A100002 1 2 1 2 3 3 1 2 4 4 3 4 1 2 5 5 3 5 1 2 4 5 3 4 1 2 1 2 3 3...
%e A100002 1 2 1 2 3 3 1 2 4 4 3 4 1 2 5 5 3 5 1 2 4 5 3 4 6 6 1 2 6 3...
%e A100002 ...
%t A100002 nn=100; t=Table[1, {nn}]; done=False; k=1; While[ !done, k++; cnt=Table[0, 
               {k-1}]; Do[If[t[[i]]<k, cnt[[t[[i]]]]++; If[Mod[cnt[[t[[i]]]], k]==0, 
               t[[i]]=k]], {i, nn}]; done=(Max[cnt]<k)]; t (T. D. Noe)
%o A100002 /* C */ #define MAXVAL 2048 /* Large enough... */ unsigned int counts[MAXVAL][MAXVAL]; 
               /* Initialized at all 0 */ unsigned int seq_value (void) /* Successive 
               calls return values in the sequence, in order. */ { unsigned int 
               value; unsigned int i; value = 1; for ( i=2; i<MAXVAL; i++ ) if ( 
               ++counts[i][value] >= i ) { counts[i][value] = 0; value = i; } return 
               value; }
%Y A100002 Cf. A100287 (first occurrence of n).
%Y A100002 Sequence in context: A071766 A007305 A112531 this_sequence A057041 A099567 
               A140530
%Y A100002 Adjacent sequences: A099999 A100000 A100001 this_sequence A100003 A100004 
               A100005
%K A100002 easy,nice,nonn
%O A100002 1,2
%A A100002 David A. Madore (david.madore(AT)ens.fr), Oct 25 2004