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 A288533 Parse A004736 into distinct phrases [1], [2], [1,3], [2,1], [4], [3], [2,1,5], [4,3], [2,1,6], ...; a(n) is the length of the n-th phrase. 1
 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 3, 2, 1, 2, 2, 2, 1, 2, 4, 1, 1, 2, 3, 3, 2, 3, 5, 1, 3, 3, 3, 1, 1, 2, 2, 4, 3, 2, 3, 4, 4, 1, 3, 4, 4, 2, 1, 2, 2, 5, 5, 1, 2, 4, 3, 5, 1, 1, 2, 3, 4, 5, 2, 2, 3, 5, 5, 3, 1, 3, 3, 3, 4, 5, 1, 2, 2, 4, 5, 6, 1, 2, 4, 4, 6, 4, 1, 2, 3, 4, 4, 6, 2, 1, 2, 3, 3, 5, 5, 4, 1, 2, 3, 5, 6, 6, 1, 1, 2, 3, 4, 5, 7, 3, 2, 3, 4, 4, 7, 6, 1, 3, 3, 4, 5, 6, 5, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The phrases are formed by the Ziv-Lempel encoding described in A106182. - Neal Gersh Tolunsky, Nov 30 2023 LINKS Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000 EXAMPLE Consider the infinite sequence [1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,...], i.e., A004736. We can first take [1] since we've never used it before. Then [2]. For the third term, we've already used [1], so we must instead take [1,3]. PROG (Python) # you should use program from internal format a = set() i = 2 s = "1" seq = "" while i < 100: j = i while j > 0: if s not in a: seq = seq + ", " + str(len(s)-len(s.replace(", ", ""))+1) a.add(s) s = str(j) else: s = s + ", " + str(j) j -= 1 i += 1 print(seq[1:]) CROSSREFS Cf. A109337, A106182, A187180, A187181, A187182, A187183, A187184, A187185, A187186, A187187, A187188, A187199, A187200. Sequence in context: A047130 A125778 A047110 * A093869 A329870 A057431 Adjacent sequences: A288530 A288531 A288532 * A288534 A288535 A288536 KEYWORD nonn AUTHOR Lewis Chen, Jun 11 2017 STATUS approved

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Last modified June 15 02:34 EDT 2024. Contains 373402 sequences. (Running on oeis4.)