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A371442
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.
4
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, 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, 10, 11, 10, 11, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12
OFFSET
0,5
COMMENTS
In other words, we keep odd-indexed bits.
For any v > 0, the value v appears A003945(A070939(v)) times in the sequence.
FORMULA
a(A000695(n)) = n.
a(A001196(n)) = n.
a(A165199(n)) = a(n).
EXAMPLE
The first terms, in decimal and in binary, are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 1 10 1
3 1 11 1
4 2 100 10
5 3 101 11
6 2 110 10
7 3 111 11
8 2 1000 10
9 2 1001 10
10 3 1010 11
11 3 1011 11
12 2 1100 10
13 2 1101 10
14 3 1110 11
15 3 1111 11
MATHEMATICA
A371442[n_] := FromDigits[IntegerDigits[n, 2][[1;; -1;; 2]], 2];
Array[A371442, 100, 0] (* Paolo Xausa, Mar 28 2024 *)
PROG
(PARI) a(n) = { my (b = binary(n)); fromdigits(vector(ceil(#b/2), k, b[2*k-1]), 2); }
(Python) def a(n): return int(bin(n)[::2], 2)
CROSSREFS
See A371459 for the sequence related to even-indexed bits.
See A059905 and A063694 for similar sequences.
Sequence in context: A258115 A296658 A276862 * A175066 A066102 A036048
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Mar 24 2024
STATUS
approved