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A090078 In binary expansion of n, reduce contiguous blocks of 0's to 0.

%I A090078 #23 Jul 30 2025 01:00:13
%S A090078 0,1,2,3,2,5,6,7,2,5,10,11,6,13,14,15,2,5,10,11,10,21,22,23,6,13,26,
%T A090078 27,14,29,30,31,2,5,10,11,10,21,22,23,10,21,42,43,22,45,46,47,6,13,26,
%U A090078 27,26,53,54,55,14,29,58,59,30,61,62,63,2,5,10,11,10,21,22,23,10,21
%N A090078 In binary expansion of n, reduce contiguous blocks of 0's to 0.
%H A090078 Amiram Eldar, <a href="/A090078/b090078.txt">Table of n, a(n) for n = 0..10000</a>
%H A090078 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%F A090078 a(a(n)) = a(n).
%F A090078 a(A090077(n)) = A090077(a(n)) = A090079(n).
%e A090078 100 -> '1100100' -> 11[00]1[00] -> 11[0]1[0] -> '11010' -> 26=a(100).
%t A090078 a[n_] := FromDigits[Flatten[Split[IntegerDigits[n, 2]] /. x_List /; x[[1]] == 0 -> {0}], 2]; Array[a, 100, 0] (* _Amiram Eldar_, Jul 30 2025 *)
%o A090078 (PARI) a(n)=my(v=binary(n),t); for(i=1,#v, if(v[i], t+=t+1, t%2, t+=t)); t \\ _Charles R Greathouse IV_, Aug 17 2016
%o A090078 (Python)
%o A090078 def a(n):
%o A090078     b = bin(n)[2:]
%o A090078     while "00" in b: b = b.replace("00", "0")
%o A090078     return int(b, 2)
%o A090078 print([a(n) for n in range(81)]) # _Michael S. Branicky_, Jul 27 2022
%Y A090078 Cf. A090077, A090079, A007088.
%K A090078 nonn,base,easy
%O A090078 0,3
%A A090078 _Reinhard Zumkeller_, Nov 20 2003