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A196168
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In binary representation of n: replace each 0 by 1, and each 1 by 10.
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4
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1, 2, 5, 10, 11, 22, 21, 42, 23, 46, 45, 90, 43, 86, 85, 170, 47, 94, 93, 186, 91, 182, 181, 362, 87, 174, 173, 346, 171, 342, 341, 682, 95, 190, 189, 378, 187, 374, 373, 746, 183, 366, 365, 730, 363, 726, 725, 1450, 175, 350, 349, 698, 347, 694, 693, 1386
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OFFSET
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0,2
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COMMENTS
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All terms are numbers with no two adjacent zeros in binary representation, cf. A003754;
a(odd) = even and a(even) = odd;
A023416(a(n)) <= A000120(a(n)), equality iff n = 2^k - 1 for k > 0;
A055010(n+1) = A196168(A000079(n));
A000120(a(n)) = A070939(n);
A023416(a(n)) = A000120(n);
A070939(a(n)) = A070939(n) + A000120(n).
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..10000
Index entries for sequences related to binary expansion of n
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FORMULA
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n = sum (b(i)*2^i: i=0..l) with 0<=b(i)<=1, L>=0, then a(n) = h(0,L) with h(v,i) = if i>L then v else h((2*v+1)*(b(i)+1),i-1)
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EXAMPLE
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n = 7 -> 111 -> 101010 -> a(7) = 42;
n = 8 -> 1000 -> 10111 -> a(8) = 23;
n = 9 -> 1001 -> 101110 -> a(9) = 46;
n = 10 -> 1010 -> 101101 -> a(10) = 45;
n = 11 -> 1011 -> 1011010 -> a(11) = 90;
n = 12 -> 1100 -> 101011 -> a(12) = 43.
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PROG
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(Haskell)
import Data.List (unfoldr)
a196168 0 = 1
a196168 n = foldl (\v b -> (2 * v + 1)*(b + 1)) 0 $ reverse $ unfoldr
(\x -> if x == 0 then Nothing else Just $ swap $ divMod x 2) n
where r v b = (2 * v + 1)*(b+1)
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CROSSREFS
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Cf. A179888, A005614.
Sequence in context: A032874 A187792 A176356 * A018514 A018288 A080792
Adjacent sequences: A196165 A196166 A196167 * A196169 A196170 A196171
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Oct 28 2011
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STATUS
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approved
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