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A082560
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a(1)=1, a(n)=2*a(n-1) if n is odd, or a(n)=a(n/2)+1 if n is even.
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4
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1, 2, 4, 3, 6, 5, 10, 4, 8, 7, 14, 6, 12, 11, 22, 5, 10, 9, 18, 8, 16, 15, 30, 7, 14, 13, 26, 12, 24, 23, 46, 6, 12, 11, 22, 10, 20, 19, 38, 9, 18, 17, 34, 16, 32, 31, 62, 8, 16, 15, 30, 14, 28, 27, 54, 13, 26, 25, 50, 24, 48, 47, 94, 7, 14, 13, 26, 12, 24, 23, 46, 11, 22, 21, 42, 20
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OFFSET
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1,2
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COMMENTS
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b(1)=1, b(n)=2*b(n/2) if n is even, or b(n)=b(n-1)+1 if n is odd produces the sequence of natural numbers.
Seen as a triangle read by rows: T(1,1) = 1; T(n+1,2*k-1) = T(n,k)+1 and T(n+1,2*k) = 2*T(n,k)+2, 1 <= k <= 2^n. - Reinhard Zumkeller, May 13 2015
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LINKS
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FORMULA
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EXAMPLE
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. 1: 1
. 2: 2 4
. 3: 3 6 5 10
. 4: 4 8 7 14 6 12 11 22
. 5: 5 10 9 18 8 16 15 30 7 14 13 26 12 24 23 46
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PROG
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(PARI) a(n)=if(n<2, 1, if(n%2, 2*a(n-1), 1+a(n/2)))
(Haskell)
a082560 n k = a082560_tabf !! (n-1) !! (k-1)
a082560_row n = a082560_tabf !! (n-1)
a082560_tabf = iterate (concatMap (\x -> [x + 1, 2 * x + 2])) [1]
a082560_list = concat a082560_tabf
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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