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A272729
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a(n) is the number of repetitions of 2n-1 in A272727.
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8
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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...
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MATHEMATICA
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Flatten@NestList[Flatten[Append[ConstantArray[1, # - 1], # + 1] & /@ #] &, {1}, 7]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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