

A329870


Runsresistance of the binary expansion of n without the first digit.


3



0, 0, 1, 2, 2, 1, 1, 3, 2, 3, 3, 2, 3, 1, 1, 3, 4, 2, 4, 2, 3, 3, 3, 3, 2, 4, 2, 4, 3, 1, 1, 3, 4, 3, 3, 4, 4, 3, 4, 5, 2, 4, 4, 5, 3, 3, 3, 3, 5, 4, 4, 2, 5, 4, 3, 4, 4, 3, 3, 4, 3, 1, 1, 3, 4, 3, 3, 4, 3, 2, 3, 3, 4, 4, 2, 3, 3, 3, 4, 5, 4, 3, 4, 2, 5, 4
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OFFSET

2,4


COMMENTS

For the operation of taking the sequence of runlengths of a finite sequence, runsresistance is defined to be the number of applications required to reach a singleton.


LINKS



EXAMPLE

Minimal representatives with each image are:
2: (0)
4: (0,0) > (2)
5: (0,1) > (1,1) > (2)
9: (0,0,1) > (2,1) > (1,1) > (2)
18: (0,0,1,0) > (2,1,1) > (1,2) > (1,1) > (2)
41: (0,1,0,0,1) > (1,1,2,1) > (2,1,1) > (1,2) > (1,1) > (2)
150: (0,0,1,0,1,1,0) > (2,1,1,2,1) > (1,2,1,1) > (1,1,2) > (2,1) > (1,1) > (2)


MATHEMATICA

Table[Length[NestWhileList[Length/@Split[#]&, Rest[IntegerDigits[n, 2]], Length[#]>1&]]1, {n, 2, 100}]


CROSSREFS

Keeping the first digit gives A318928.
Compositions counted by runsresistance are A329744.


KEYWORD

nonn


AUTHOR



STATUS

approved



