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 A293843 Split the infinite binary word A030302, from left to right, into the largest possible cubefree chunks; a(n) = length of n-th cubefree chunk. 3
 5, 7, 4, 4, 10, 3, 9, 5, 2, 3, 5, 12, 9, 10, 2, 3, 7, 9, 2, 5, 4, 2, 4, 2, 4, 2, 4, 6, 6, 3, 8, 15, 6, 12, 5, 2, 14, 2, 6, 2, 4, 6, 3, 11, 13, 8, 2, 2, 4, 3, 5, 7, 4, 2, 6, 5, 2, 5, 2, 2, 3, 2, 5, 2, 5, 7, 4, 3, 7, 7, 7, 3, 7, 15, 7, 19, 7, 2, 5, 7, 11, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Using A030190 instead of A030302 leads to the same sequence except for the first term (that would equal 6). The word A030302 contains infinitely many consecutive triples of 0's (corresponding for example to the last binary digits of multiples of 8), hence A030302 has no infinite cubefree suffix, and this sequence is well defined for any n > 0. a(n) >= 2 for any n > 0. This sequence is unbounded: for any n > 0: - A028445(2*n) > 0, - hence we can choose a number in A286262, say c, with 2*n digits in binary, - and the subword of A030302 corresponding to c will participate in no more than two cubefree chunks, - and one of those chunks will have at least length n, QED. The first records of the sequence are (see also A293867 and A293868): a(n)  n ----  -- 5     1 7     2 10    5 12    12 15    32 19    76 21    212 25    412 35    418 36    2305 39    5118 47    5516 59    49014 63    104902 67    261530 71    478638 75    1016483 79    2148745 83    4532050 87    9534639 91    20011894 95    41896466 LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PERL program for A293843 EXAMPLE The following table shows the first terms of the sequence, alongside the corresponding cubefree chunks: n   a(n)  n-th chunk --  ----  ---------- 1   5     11011 2   7          1001011 3   4                 1011 4   4                     1100 5   10                        0100110101 6   3                                   011 7   9                                      110011011 8   5                                               11011 9   2                                                    11 10  3                                                      100 CROSSREFS Cf. A028445, A030190, A030302, A286262, A293867, A293868. Sequence in context: A011497 A010488 A300081 * A240946 A343039 A021178 Adjacent sequences:  A293840 A293841 A293842 * A293844 A293845 A293846 KEYWORD nonn,base AUTHOR Rémy Sigrist, Oct 17 2017 STATUS approved

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Last modified June 22 14:15 EDT 2021. Contains 345380 sequences. (Running on oeis4.)