A374849 - OEIS

%I #28 Oct 01 2024 08:50:44

%S 0,1,0,1,1,0,0,1,2,3,1,0,0,1,0,1,1,2,2,3,3,1,1,0,0,0,0,1,1,0,0,1,2,3,

%T 1,2,4,5,2,3,6,7,3,1,2,3,1,0,0,1,0,0,0,1,0,1,2,3,1,0,0,1,0,1,1,2,2,3,

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

%N In the binary expansion of n: collapse bits from most to least significant 10 -> 1, 01 -> 0, 00 -> nothing, 11 -> nothing.

%C This is essentialy the Von Neumann biased to fair coin extractor.

%C a(n) = 0 if the collapse results in no bits.

%C If the bit size of n is odd then the least significant bit is ignored.

%H Paolo Xausa, <a href="/A374849/b374849.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Fair_coin">Fair coin</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Randomness_extractor">Randomness extractor</a>.

%e For n = 27983, the bits of n collapse as

%e   n    = binary 11 01 10 10 10 01 11 1

%e   a(n) = binary    0  1  1  1  0  = 14

%t A374849[n_] := FromDigits[StringReplace[IntegerString[n, 2], {"01"->"0", "10"->"1", Repeated[_, 2]->""}], 2];

%t Array[A374849, 100] (* _Paolo Xausa_, Oct 01 2024 *)

%o (Python)

%o def a(n):

%o   e, B = "", bin(n)[2:]

%o   for i in range(0,len(B),2):

%o       if B[i:i+2] == "10": e += "1"

%o       if B[i:i+2] == "01": e += "0"

%o   if e == '': return 0

%o   return int(e,2)

%o print([a(n) for n in range(1,70)])

%K nonn,base,easy

%O 1,9

%A _Darío Clavijo_, Sep 16 2024