A156242 Bisection of A054353.

3, 6, 9, 12, 15, 19, 21, 24, 27, 30, 33, 36, 39, 42, 45, 47, 50, 54, 57, 60, 63, 66, 69, 72, 75, 77, 81, 84, 87, 90, 93, 96, 100, 102, 105, 108, 111, 114, 117, 120, 123, 127, 129, 132, 136, 139, 142, 145, 147, 151, 154, 156, 159, 163, 166, 169, 172, 174, 177, 181

Offset: 1

Author

Benoit Cloitre, Feb 07 2009

Keywords

• nonn

Comments

Positions of strict descents in the Kolakoski sequence A000002. Strict ascents are A156243. - Gus Wiseman, Mar 31 2020

Crossrefs

Cf. A000002, A156243.

The version for prime gaps is A258026.

Sizes of maximal weakly increasing subsequences of A000002 are A332875.

Cf. A054804, A124766, A124769, A225620, A238343, A332273, A333213, A333215, A333256, A333383.

Programs

Mathematica

kolagrow[q_]:=If[Length[q]<2,Take[{1,2},Length[q]+1],Append[q,Switch[{q[[Length[Split[q]]]],q[[-2]],Last[q]},{1,1,1},0,{1,1,2},1,{1,2,1},2,{1,2,2},0,{2,1,1},2,{2,1,2},2,{2,2,1},1,{2,2,2},1]]]
kol[n_Integer]:=Nest[kolagrow,{1},n-1];
Join@@Position[Partition[kol[100],2,1],{2,1}] (* Gus Wiseman, Mar 31 2020 *)

Formula

a(n) = A054353(2n).

A000002(a(n))=2 and A000002(a(n)+1)=1. - Jon Perry, Sep 04 2012