|
%I #29 May 11 2021 09:06:45
%S 0,2,4,6,8,10,14,16,18,20,22,24,26,28,30,36,38,40,42,44,46,48,50,54,
%T 56,58,60,62,64,68,70,72,74,76,78,80,82,86,88,98,104,106,116,118,122,
%U 124,126,128,130,132,136,138,140,142,144,146,148,150,152,158
%N Exactly half of first a(n) terms of Kolakoski sequence A000002 are 1's (not known to be infinite).
%C The sequences A022292, A074261, and A342799 partition the nonnegative integers. - _Clark Kimberling_, May 10 2021
%H Joerg Arndt, <a href="/A022292/b022292.txt">Table of n, a(n) for n = 0..8739</a>
%F Conjecture: a(n) is asymptotic to c*n*log(n) for some constant c <= 1. - _Benoit Cloitre_, Nov 17 2003
%t k = Prepend[Nest[Flatten[Partition[#, 2] /. {{2, 2} -> {2, 2, 1, 1}, {2, 1} -> {2, 2, 1}, {1, 2} -> {2, 1, 1}, {1, 1} -> {2, 1}}] &, {2, 2}, 14], 1]; (* A000002 *)
%t Select[Range[400], Count[Take[k, #], 1] < #/2 &] (* A074261 *)
%t Select[Range[400], Count[Take[k, #], 1] == #/2 &] (* A022292 *)
%t Select[Range[400], Count[Take[k, #], 1] > #/2 &] (* A342799 *)
%t (* _Clark Kimberling_, May 10 2021 *)
%o (JavaScript)
%o a=new Array();
%o a[1]=1; a[2]=2; a[3]=2; cd=1; ap=3;
%o for (i=4; i<1000; i++)
%o {
%o if (a[ap]==1) a[i]=cd;
%o else {a[i]=cd; a[i+1]=cd; i++}
%o ap++;
%o cd=3-cd;
%o }
%o oc=0; tc=0;
%o for (i=1; i<1000; i++)
%o {
%o if (oc==tc) document.write(i-1+", ");
%o if (a[i]==1) oc++;
%o else tc++;
%o }
%o // _Jon Perry_, Sep 11 2012
%Y Cf. A000002, A074261, A022293, A342799.
%K nonn
%O 0,2
%A _Clark Kimberling_
%E 0 prepended by _Jon Perry_, Sep 11 2012
|
