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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 A021178 A201506

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 July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)