A090080 -id:A090080

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A090079

In binary expansion of n: reduce contiguous blocks of 0's to 0 and contiguous blocks of 1's to 1.

+10
10

0, 1, 2, 1, 2, 5, 2, 1, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 10, 21, 42, 21, 10, 21, 10, 5, 2, 5, 10, 5, 10, 21, 10, 5, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 10, 21, 42, 21, 10, 21, 10, 5, 10, 21, 42, 21

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OFFSET

0,3

COMMENTS

a(a(n))=a(n); a(n)=A090078(A090077(n))=A090077(A090078(n)).

All terms are without consecutive equal binary digits: a(A000975(n)) = A000975(n) and a(m) <> A000975(n) for m < A000975(n). - Reinhard Zumkeller, Feb 16 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to binary expansion of n

FORMULA

Conjecture: a(n) = (2^(A005811(n)+1) + (1-(-1)^n)/2 - 2)/3. - Velin Yanev, Dec 12 2016

EXAMPLE

100 -> '1100100' -> [11][00][1][00] -> [1][0][1][0] -> '1010' ->

10=a(100).

MATHEMATICA

Table[FromDigits[#, 2] &@ Map[First, Split@ IntegerDigits[n, 2]], {n, 0, 83}] (* Michael De Vlieger, Dec 12 2016 *)

FromDigits[Split[IntegerDigits[#, 2]][[All, 1]], 2]&/@Range[0, 90] (* Harvey P. Dale, Oct 10 2017 *)

PROG