cp's OEIS Frontend

A288576 The Fibonacci word in A104324 partitioned into blocks.

%I A288576 #16 Jan 31 2024 13:08:08
%S A288576 0,1,22,323,42344,52344545,6234454564566,723445456456674566767,
%T A288576 8234454564566745667678456676786788,
%U A288576 9234454564566745667678456676786788945667678678896788989
%N A288576 The Fibonacci word in A104324 partitioned into blocks.
%C A288576 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 A288576 Jiemeng Zhang, Zhixiong Wen, and Wen Wu, <a href="https://doi.org/10.37236/6745">Some Properties of the Fibonacci Sequence on an Infinite Alphabet</a>, Electronic Journal of Combinatorics, 24(2) (2017), #P2.52.
%e A288576 The initial blocks are as follows:
%e A288576  0,
%e A288576  1,
%e A288576  22,
%e A288576  323,
%e A288576  42344,
%e A288576  52344545,
%e A288576  6234454564566,
%e A288576  723445456456674566767,
%e A288576  8234454564566745667678456676786788,
%e A288576  9234454564566745667678456676786788945667678678896788989,
%e A288576  ...
%e A288576 but if the commas are inserted (as they should be) then we see the blocks more clearly:
%e A288576  0,
%e A288576  1,
%e A288576  2,2,
%e A288576  3,2,3,
%e A288576  4,2,3,4,4,
%e A288576  5,2,3,4,4,5,4,5,
%e A288576  6,2,3,4,4,5,4,5,6,4,5,6,6,
%e A288576  7,2,3,4,4,5,4,5,6,4,5,6,6,7,4,5,6,6,7,6,7,
%e A288576  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 A288576  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 A288576  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 A288576 ...
%Y A288576 Block n has length Fibonacci(n), see A000045.
%K A288576 nonn,tabf,base
%O A288576 0,3
%A A288576 _N. J. A. Sloane_, Jun 30 2017