A272729 a(n) is the number of repetitions of 2n-1 in A272727.

1, 2, 1, 3, 2, 1, 1, 4, 1, 3, 2, 2, 1, 1, 1, 5, 2, 1, 1, 4, 1, 3, 1, 3, 2, 2, 2, 1, 1, 1, 1, 6, 1, 3, 2, 2, 1, 1, 1, 5, 2, 1, 1, 4, 2, 1, 1, 4, 1, 3, 1, 3, 1, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 7, 2, 1, 1, 4, 1, 3, 1, 3, 2, 2, 2, 1, 1, 1, 1, 6, 1, 3, 2, 2, 1, 1, 1, 5, 1, 3, 2, 2, 1, 1, 1, 5

Offset: 1

Author

Ivan Neretin, May 05 2016

Keywords

• nonn

Comments

Also, value of A272728 at the n-th local maximum.

Also, the trajectory of 1 under the morphism n->[1,1..1,n+1] (the number of 1's is n-1).

Average value tends to 2.

Number n makes its first appearance at the position 2^(n-1) and has frequency 1/2^n.

Conjectured first differences of A037988 (true for at least 8192 terms). - Sean A. Irvine, Jun 26 2022

Examples

			The morphism acts as follows:
1->2; 2->1,3; 3->1,1,4; 4->1,1,1,5; etc.
The trajectory starts as:
1 ->
2 ->
1,3 ->
2,1,1,4 ->
1,3,2,2,1,1,1,5 -> ...
The result of k iterations is a series with 2^(k-1) terms; their sum is 2^k.
If A001511 is laid out in a similar irregular triangle, each row
would contain the same terms, albeit in a different order:
1,
2,
1,3,
1,2,1,4,
1,2,1,3,1,2,1,5...
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A001511, A272727, A272728.

Programs

Mathematica

Flatten@NestList[Flatten[Append[ConstantArray[1, # - 1], # + 1] & /@ #] &, {1}, 7]