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A333229 First sums of the Kolakoski sequence A000002. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)