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A337821
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For n >= 0, a(4n+1) = 0, a(4n+3) = a(2n+1) + 1, a(2n+2) = a(n+1).
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3
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0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 2, 3, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 0, 3, 4, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 2, 3, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 0, 1, 3, 0, 4, 5, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 2, 3, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 0, 3, 4, 1
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OFFSET
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1,7
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COMMENTS
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This sequence is the ruler sequence A007814 interleaved with this sequence; specifically, the odd bisection is A007814, the even bisection is the sequence itself.
The 3-adic valuation of the Doudna sequence (A005940).
The 2-adic valuation of Kimberling's paraphrases (A003602).
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LINKS
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FORMULA
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a(2*n) = a(n).
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EXAMPLE
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Start of table showing the interleaving with ruler sequence, A007814:
((n+1)/2)
1 0 0
2 0 0
3 1 1
4 0 0
5 0 0
6 1 1
7 2 2
8 0 0
9 0 0
10 0 0
11 1 1
12 1 1
13 0 0
14 2 2
15 3 3
16 0 0
17 0 0
18 0 0
19 1 1
20 0 0
21 0 0
22 1 1
23 2 2
24 1 1
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MATHEMATICA
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a[n_] := IntegerExponent[(n/2^IntegerExponent[n, 2] + 1)/2, 2]; Array[a, 100] (* Amiram Eldar, Sep 30 2020 *)
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PROG
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(PARI) a(n) = valuation(n>>valuation(n, 2)+1, 2) - 1; \\ Kevin Ryde, Apr 06 2024
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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