A329356 - OEIS

%I #29 Jan 03 2023 10:17:03

%S 0,1,2,4,9,19,38,77,154,308,617,1234,2468,4937,9875,19750,39501,79003,

%T 158006,316012,632025,1264050,2528101,5056203,10112406,20224813,

%U 40449626,80899252,161798505,323597011,647194022,1294388045,2588776091,5177552182,10355104365

%N The binary expansion of a(n) is the first n terms of 2 - A000002.

%F a(n) = floor((1-c/2)*2^n), where c = A118270 is the Kolakoski constant. - _Lorenzo Sauras Altuzarra_, Jan 01 2023

%e a(7) = 77 has binary expansion q = {1, 0, 0, 1, 1, 0, 1}, and 2 - q is {1, 2, 2, 1, 1, 2, 1}, which is the first 7 terms of A000002.

%t 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]]]

%t kol[n_Integer]:=If[n==0,{},Nest[kolagrow,{1},n-1]];

%t Table[FromDigits[2-kol[n],2],{n,0,30}]

%Y Cf. A118270, A329361.

%Y Replacing "2 - A000002" with "A000002 - 1" gives A329355.

%Y Initial subsequences of A000002 are A329360.

%Y Cf. A121016, A211100, A275692, A296658, A329315, A329316, A329317, A329362.

%K nonn,easy

%O 0,3

%A _Gus Wiseman_, Nov 12 2019