A022292 Exactly half of first a(n) terms of Kolakoski sequence A000002 are 1's (not known to be infinite).

0, 2, 4, 6, 8, 10, 14, 16, 18, 20, 22, 24, 26, 28, 30, 36, 38, 40, 42, 44, 46, 48, 50, 54, 56, 58, 60, 62, 64, 68, 70, 72, 74, 76, 78, 80, 82, 86, 88, 98, 104, 106, 116, 118, 122, 124, 126, 128, 130, 132, 136, 138, 140, 142, 144, 146, 148, 150, 152, 158

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

Cf. A000002, A074261, A022293, A342799.

Sequence in context: A302979 A006586 A260391 * A225241 A087370 A364158

Adjacent sequences: A022289 A022290 A022291 * A022293 A022294 A022295

Keyword

nonn

Author

Clark Kimberling

Extensions

0 prepended by Jon Perry, Sep 11 2012

Status

approved