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 A107750 If n=0 then 0, else smallest number greater than its predecessor and having either more or fewer zeros in its binary representation. 3
 0, 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 92, 93 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Essentially the complement of A016825 with respect to the nonnegative integers (except for 2). A023416(a(n+1)) <> A023416(a(n)). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Index entries for sequences related to binary expansion of n FORMULA a(n+1) = a(n) + A107751(n). For k >= 0, 0 <= i <= 3*2^k: a(6*2^k + i) = a(3*2^k + i) + 4*2^k, a(9*2^k + i) = a(3*2^k + i) + 8*2^k. a(n) = n - sign(floor(n/3)) + floor( (1/2)*sum_{i=1..n} ( ceiling((i+2)/3) - floor((i+2)/3) ) ). - Wesley Ivan Hurt, Jun 16 2014 Conjectures from Colin Barker, Jul 24 2017: (Start) G.f.: x*(1+x)*(1+x^2-x^3+x^4) / ((1-x)^2*(1+x+x^2)). a(n) = a(n-1) + a(n-3) - a(n-4) for n>3. (End) MATHEMATICA Table[n - Sign[Floor[n/3]] + Floor[(1/2) Sum[Ceiling[(i + 2)/3] - Floor[(i + 2)/3], {i, n}]], {n, 0, 50}] (* Wesley Ivan Hurt, Jun 16 2014 *) PROG (Haskell) a107750 n = a107750_list !! n a107750_list = 0 : f 0 where f x = y : f y where y = head [z | z <- [x + 1 ..], a023416 z /= a023416 x] -- Reinhard Zumkeller, Jul 07 2014 CROSSREFS Cf. A107686, A007088, A023416. Sequence in context: A247915 A284676 A187681 * A196736 A284946 A285901 Adjacent sequences: A107747 A107748 A107749 * A107751 A107752 A107753 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 23 2005 STATUS approved

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Last modified June 6 20:05 EDT 2023. Contains 363151 sequences. (Running on oeis4.)