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A371442
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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.
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3
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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
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OFFSET
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0,5
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COMMENTS
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In other words, we keep odd-indexed bits.
For any v > 0, the value v appears A003945(A070939(v)) times in the sequence.
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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A371442[n_] := FromDigits[IntegerDigits[n, 2][[1;; -1;; 2]], 2];
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PROG
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(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)
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CROSSREFS
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See A371459 for the sequence related to even-indexed bits.
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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