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
Keywords
Links
- Joerg Arndt, Table of n, a(n) for n = 0..8739
Programs
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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 -
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 *)
Formula
Conjecture: a(n) is asymptotic to c*n*log(n) for some constant c <= 1. - Benoit Cloitre, Nov 17 2003
Extensions
0 prepended by Jon Perry, Sep 11 2012
Comments