A329356 The binary expansion of a(n) is the first n terms of 2 - A000002.

0, 1, 2, 4, 9, 19, 38, 77, 154, 308, 617, 1234, 2468, 4937, 9875, 19750, 39501, 79003, 158006, 316012, 632025, 1264050, 2528101, 5056203, 10112406, 20224813, 40449626, 80899252, 161798505, 323597011, 647194022, 1294388045, 2588776091, 5177552182, 10355104365

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Formula

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

Example

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.

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]:=If[n==0, {}, Nest[kolagrow, {1}, n-1]];
Table[FromDigits[2-kol[n], 2], {n, 0, 30}]

Crossrefs

Cf. A118270, A329361.

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

Initial subsequences of A000002 are A329360.

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

Sequence in context: A309267 A262864 A129784 * A125050 A056186 A265387

Adjacent sequences: A329353 A329354 A329355 * A329357 A329358 A329359

Keyword

nonn,easy

Author

Gus Wiseman, Nov 12 2019

Status

approved