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A371459
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For any positive integer with binary digits (b_1, ..., b_w) (where b_1 = 1), the binary digits of a(n), possibly with leading zeros, are (b_2, b_4, ..., b_{floor(w/2) * 2}); a(0) = 0.
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2
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0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 3, 2, 3, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 0, 1, 0, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 4, 5, 4, 5, 6, 7, 6, 7, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 0, 0, 1, 1, 0, 0, 1
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OFFSET
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0,13
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COMMENTS
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In other words, we keep even-indexed bits.
Every integer appears infinitely many 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 0 1 0
2 0 10 0
3 1 11 1
4 0 100 0
5 0 101 0
6 1 110 1
7 1 111 1
8 0 1000 0
9 1 1001 1
10 0 1010 0
11 1 1011 1
12 2 1100 10
13 3 1101 11
14 2 1110 10
15 3 1111 11
16 0 10000 0
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MATHEMATICA
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A371459[n_] := FromDigits[IntegerDigits[n, 2][[2;; -1;; 2]], 2];
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PROG
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(PARI) a(n) = { my (b = binary(n)); fromdigits(vector(#b\2, k, b[2*k]), 2); }
(Python)
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CROSSREFS
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See A371442 for the sequence related to odd-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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