A107750 If n=0 then 0, else smallest number greater than its predecessor and having either more or fewer zeros in its binary representation.

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

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