A333229 First sums of the Kolakoski sequence A000002.

3, 4, 3, 2, 3, 3, 3, 4, 3, 3, 4, 3, 2, 3, 3, 2, 3, 4, 3, 3, 3, 2, 3, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 4, 3, 3, 3, 2, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 3, 3, 3, 4, 3, 3, 4, 3, 2, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 2, 3, 4, 3, 3, 4, 3, 2, 3, 3

Offset

1,1

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = A000002(n) + A000002(n + 1).

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];
Table[kol[n][[-1]]+kol[n+1][[-1]], {n, 30}]

Crossrefs

Positions of 3's are A054353.

Positions of 2's are A074262.

Positions of 4's are A074263.

The number of runs in the first n terms of A000002 is A156253(n).

Even-indexed terms are A332273 (without the first term).

Odd-indexed terms are A332875.

Cf. A000002, A001462, A013947, A013948, A088568, A156728, A288605, A296658, A329315, A329316, A329317, A329362.

Sequence in context: A280136 A258451 A332412 * A164358 A275638 A281975

Adjacent sequences: A333226 A333227 A333228 * A333230 A333231 A333232

Keyword

nonn

Author

Gus Wiseman, Mar 18 2020

Status

approved