|
%I #33 Mar 28 2024 18:04:09
%S 0,1,1,1,2,3,2,3,2,2,3,3,2,2,3,3,4,5,4,5,6,7,6,7,4,5,4,5,6,7,6,7,4,4,
%T 5,5,4,4,5,5,6,6,7,7,6,6,7,7,4,4,5,5,4,4,5,5,6,6,7,7,6,6,7,7,8,9,8,9,
%U 10,11,10,11,8,9,8,9,10,11,10,11,12,13,12
%N For any positive integer n with binary digits (b_1, ..., b_w) (where b_1 = 1), the binary digits of a(n) are (b_1, b_3, ..., b_{2*ceiling(w/2)-1}); a(0) = 0.
%C In other words, we keep odd-indexed bits.
%C For any v > 0, the value v appears A003945(A070939(v)) times in the sequence.
%H Rémy Sigrist, <a href="/A371442/b371442.txt">Table of n, a(n) for n = 0..8192</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(A000695(n)) = n.
%F a(A001196(n)) = n.
%F a(A165199(n)) = a(n).
%e The first terms, in decimal and in binary, are:
%e n a(n) bin(n) bin(a(n))
%e -- ---- ------ ---------
%e 0 0 0 0
%e 1 1 1 1
%e 2 1 10 1
%e 3 1 11 1
%e 4 2 100 10
%e 5 3 101 11
%e 6 2 110 10
%e 7 3 111 11
%e 8 2 1000 10
%e 9 2 1001 10
%e 10 3 1010 11
%e 11 3 1011 11
%e 12 2 1100 10
%e 13 2 1101 10
%e 14 3 1110 11
%e 15 3 1111 11
%t A371442[n_] := FromDigits[IntegerDigits[n, 2][[1;;-1;;2]], 2];
%t Array[A371442, 100, 0] (* _Paolo Xausa_, Mar 28 2024 *)
%o (PARI) a(n) = { my (b = binary(n)); fromdigits(vector(ceil(#b/2), k, b[2*k-1]), 2); }
%o (Python) def a(n): return int(bin(n)[::2], 2)
%Y See A371459 for the sequence related to even-indexed bits.
%Y See A059905 and A063694 for similar sequences.
%Y Cf. A000695, A001196, A003945, A070939, A165199, A371461.
%K nonn,base,easy
%O 0,5
%A _Rémy Sigrist_, Mar 24 2024
|
