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A288576 The Fibonacci word in A104324 partitioned into blocks. 1

%I

%S 0,1,22,323,42344,52344545,6234454564566,723445456456674566767,

%T 8234454564566745667678456676786788,

%U 9234454564566745667678456676786788945667678678896788989

%N The Fibonacci word in A104324 partitioned into blocks.

%C This way of representing the block structure of A104324 is used by Zhang et al. (2017), but of course only makes sense for blocks 0 through 9.

%H Jiemeng Zhang, Zhixiong Wen, Wen Wu, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p52">Some Properties of the Fibonacci Sequence on an Infinite Alphabet</a>, Electronic Journal of Combinatorics, 24(2) (2017), #P2.52.

%e The initial blocks are as follows:

%e 0,

%e 1,

%e 22,

%e 323,

%e 42344,

%e 52344545,

%e 6234454564566,

%e 723445456456674566767,

%e 8234454564566745667678456676786788,

%e 9234454564566745667678456676786788945667678678896788989,

%e ...

%e but if the commas are inserted (as they should be) then we see the blocks more clearly:

%e 0,

%e 1,

%e 2,2,

%e 3,2,3,

%e 4,2,3,4,4,

%e 5,2,3,4,4,5,4,5,

%e 6,2,3,4,4,5,4,5,6,4,5,6,6,

%e 7,2,3,4,4,5,4,5,6,4,5,6,6,7,4,5,6,6,7,6,7,

%e 8,2,3,4,4,5,4,5,6,4,5,6,6,7,4,5,6,6,7,6,7,8,4,5,6,6,7,6,7,8,6,7,8,8,

%e 9,2,3,4,4,5,4,5,6,4,5,6,6,7,4,5,6,6,7,6,7,8,4,5,6,6,7,6,7,8,6,7,8,8,9,4,5,6,6,7,6,7,8,6,7,8,8,9,6,7,8,8,9,8,9,

%e 10,2,3,4,4,5,4,5,6,4,5,6,6,7,4,5,6,6,7,6,7,8,4,5,6,6,7,6,7,8,6,7,8,8,9,4,5,6,6,7,6,7,8,6,7,8,8,9,6,7,8,8,9,8,9,10,4,5,6,6,7,6,7,8,6,7,8,8,9,6,7,8,8,9,8,9,10,6,7,8,8,9,8,9,10,8,9,10,10,

%e ...

%Y Block n has length Fibonacci(n), see A000045.

%K nonn,tabf,base

%O 0,3

%A _N. J. A. Sloane_, Jun 30 2017

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Last modified April 1 12:18 EDT 2020. Contains 333159 sequences. (Running on oeis4.)