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A054352
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Lengths of successive generations of the Kolakoski sequence A000002.
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11
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1, 2, 4, 7, 11, 18, 28, 43, 65, 99, 150, 226, 340, 511, 768, 1153, 1728, 2590, 3885, 5826, 8742, 13116, 19674, 29514, 44280, 66431, 99667, 149531, 224306, 336450, 504648, 756961, 1135450, 1703197, 2554846, 3832292, 5748474, 8622646, 12933971, 19400955, 29101203
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OFFSET
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0,2
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COMMENTS
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Starting with a(0) = 1, the first term of A000002, the n-th generation is the run of figures directly generated from the preceding generation completed with a single last figure which begins the next run. Thus a(0) = 1 -> 1-2 -> 1-22-1 -> 1-2211-2-1 etc. - Jean-Christophe Hervé, Oct 26 2014
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LINKS
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FORMULA
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MATHEMATICA
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A2 = {1, 2, 2}; Do[If[Mod[n, 10^5] == 0, Print["n = ", n]]; m = 1 + Mod[n - 1, 2]; an = A2[[n]]; A2 = Join[A2, Table[m, {an}]], {n, 3, 10^6}]; A054353 = Accumulate[A2]; Clear[a]; a[0] = 1; a[n_] := a[n] = A054353[[a[n - 1]]] + 1; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Oct 30 2014, after Jean-Christophe Hervé *)
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PROG
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(Python)
def aupton(nn):
K = Kolakoski() # using Kolakoski() in A000002
for n in range(2, nn+1):
target = alst[-1]
while idx <= target:
idx += 1
return alst
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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