OFFSET
0,2
COMMENTS
The sequences A022292, A074261, and A342799 partition the nonnegative integers. - Clark Kimberling, May 10 2021
LINKS
Joerg Arndt, Table of n, a(n) for n = 0..8739
FORMULA
Conjecture: a(n) is asymptotic to c*n*log(n) for some constant c <= 1. - Benoit Cloitre, Nov 17 2003
MATHEMATICA
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 *)
Select[Range[400], Count[Take[k, #], 1] < #/2 &] (* A074261 *)
Select[Range[400], Count[Take[k, #], 1] == #/2 &] (* A022292 *)
Select[Range[400], Count[Take[k, #], 1] > #/2 &] (* A342799 *)
(* Clark Kimberling, May 10 2021 *)
PROG
(JavaScript)
a=new Array();
a[1]=1; a[2]=2; a[3]=2; cd=1; ap=3;
for (i=4; i<1000; i++)
{
if (a[ap]==1) a[i]=cd;
else {a[i]=cd; a[i+1]=cd; i++}
ap++;
cd=3-cd;
}
oc=0; tc=0;
for (i=1; i<1000; i++)
{
if (oc==tc) document.write(i-1+", ");
if (a[i]==1) oc++;
else tc++;
}
// Jon Perry, Sep 11 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
0 prepended by Jon Perry, Sep 11 2012
STATUS
approved