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 A196168 In binary representation of n: replace each 0 by 1, and each 1 by 10. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). LINKS _Reinhard Zumkeller_, Table of n, a(n) for n = 0..10000 FORMULA 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) EXAMPLE 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. PROG (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) CROSSREFS Cf. A179888, A005614. Sequence in context: A032874 A187792 A176356 * A018514 A018288 A080792 Adjacent sequences:  A196165 A196166 A196167 * A196169 A196170 A196171 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 28 2011 STATUS approved

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