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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
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
(PARI) a(n) = if(n--, bitneg(n, 2+logint(n, 2)), 1); \\ Kevin Ryde, Apr 14 2021
CROSSREFS
Cf. A004754 (terms sorted), A008687 (binary weight).
Sequence in context: A069913 A326002 A072403 * A074639 A319525 A357983
KEYWORD
base,nonn
AUTHOR
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)