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A010078 Shortest representation of -n in 2's-complement format. 4
1, 2, 5, 4, 11, 10, 9, 8, 23, 22, 21, 20, 19, 18, 17, 16, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 191, 190, 189 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..8192

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

a(n) = 2^(ceiling(log_2(n)+1)) - n.

a(n) = b(n-1), where b(n) = 1 if n = 0, otherwise 2*b(floor(n/2)) + 1 - n mod 2. - Reinhard Zumkeller, Feb 19 2003

G.f.: (x/(1-x)) * (1/x + Sum_{k>=0} 2^k*(x^2^k + 2x^2^(k+1))/(1+x^2^k)). - Ralf Stephan, Jun 15 2003

a(1) = 1; for n > 1, a(2n-1) = 2*a(n) + 1; for n >= 1, a(2n) = 2*a(n). - Philippe Deléham, Feb 29 2004

MATHEMATICA

Array[2^(Ceiling[Log2[#] + 1]) - # &, 67] (* Michael De Vlieger, Oct 15 2018 *)

PROG

(Haskell)

a010078 = x . subtract 1 where

   x m = if m == 0 then 1 else 2 * x m' + 1 - b

            where (m', b) = divMod m 2

-- Reinhard Zumkeller, Feb 21 2014

CROSSREFS

Cf. A004754, A008687.

Sequence in context: A100710 A069913 A072403 * A074639 A319525 A002314

Adjacent sequences:  A010075 A010076 A010077 * A010079 A010080 A010081

KEYWORD

base,nonn

AUTHOR

Leonid Broukhis

STATUS

approved

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Last modified December 10 01:59 EST 2018. Contains 318035 sequences. (Running on oeis4.)