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A377404 In the binary expansion of n, replace the first, third, fifth, etc. 1's by 0's.

%I A377404 #12 Oct 31 2024 01:28:24
%S A377404 0,0,0,1,0,1,2,2,0,1,2,2,4,4,4,5,0,1,2,2,4,4,4,5,8,8,8,9,8,9,10,10,0,
%T A377404 1,2,2,4,4,4,5,8,8,8,9,8,9,10,10,16,16,16,17,16,17,18,18,16,17,18,18,
%U A377404 20,20,20,21,0,1,2,2,4,4,4,5,8,8,8,9,8,9,10,10
%N A377404 In the binary expansion of n, replace the first, third, fifth, etc. 1's by 0's.
%C A377404 Each 1 in the binary expansion of n appears either in a(n) or in A265263(n).
%H A377404 Rémy Sigrist, <a href="/A377404/b377404.txt">Table of n, a(n) for n = 0..8192</a>
%H A377404 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A377404 a(n) = n - A265263(n).
%F A377404 a(2*n) = 2*a(n).
%F A377404 A000120(a(n)) = floor(A000120(n)/2).
%e A377404 The first terms, in decimal and in binary, are:
%e A377404   n   a(n)  bin(n)  bin(a(n))
%e A377404   --  ----  ------  ---------
%e A377404    0     0       0          0
%e A377404    1     0       1          0
%e A377404    2     0      10          0
%e A377404    3     1      11          1
%e A377404    4     0     100          0
%e A377404    5     1     101          1
%e A377404    6     2     110         10
%e A377404    7     2     111         10
%e A377404    8     0    1000          0
%e A377404    9     1    1001          1
%e A377404   10     2    1010         10
%e A377404   11     2    1011         10
%e A377404   12     4    1100        100
%e A377404   13     4    1101        100
%e A377404   14     4    1110        100
%e A377404   15     5    1111        101
%o A377404 (PARI) a(n) = { my (b = binary(n), h = 0); for (i = 1, #b, if (b[i] && h++%2==1, b[i]
%o A377404 = 0;);); fromdigits(b, 2); }
%Y A377404 Cf. A000120, A265263.
%K A377404 nonn,base,easy
%O A377404 0,7
%A A377404 _Rémy Sigrist_, Oct 28 2024