OFFSET
1,2
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
LINKS
EXAMPLE
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...
MATHEMATICA
Flatten@NestList[Flatten[Append[ConstantArray[1, # - 1], # + 1] & /@ #] &, {1}, 7]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ivan Neretin, May 05 2016
STATUS
approved