A288576 The Fibonacci word in A104324 partitioned into blocks.

0, 1, 22, 323, 42344, 52344545, 6234454564566, 723445456456674566767, 8234454564566745667678456676786788, 9234454564566745667678456676786788945667678678896788989

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..9.

Jiemeng Zhang, Zhixiong Wen, and Wen Wu, Some Properties of the Fibonacci Sequence on an Infinite Alphabet, Electronic Journal of Combinatorics, 24(2) (2017), #P2.52.

Example

The initial blocks are as follows:
 0,
 1,
 22,
 323,
 42344,
 52344545,
 6234454564566,
 723445456456674566767,
 8234454564566745667678456676786788,
 9234454564566745667678456676786788945667678678896788989,
 ...
but if the commas are inserted (as they should be) then we see the blocks more clearly:
 0,
 1,
 2,2,
 3,2,3,
 4,2,3,4,4,
 5,2,3,4,4,5,4,5,
 6,2,3,4,4,5,4,5,6,4,5,6,6,
 7,2,3,4,4,5,4,5,6,4,5,6,6,7,4,5,6,6,7,6,7,
 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,
 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,
 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,
...

Crossrefs

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

Sequence in context: A021904 A022343 A025945 * A020571 A021874 A025963

Adjacent sequences: A288573 A288574 A288575 * A288577 A288578 A288579

Keyword

nonn,tabf,base

Author

N. J. A. Sloane, Jun 30 2017

Status

approved