login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A263017 n is the a(n)-th positive integer having its binary weight. 11
1, 2, 1, 3, 2, 3, 1, 4, 4, 5, 2, 6, 3, 4, 1, 5, 7, 8, 5, 9, 6, 7, 2, 10, 8, 9, 3, 10, 4, 5, 1, 6, 11, 12, 11, 13, 12, 13, 6, 14, 14, 15, 7, 16, 8, 9, 2, 15, 17, 18, 10, 19, 11, 12, 3, 20, 13, 14, 4, 15, 5, 6, 1, 7, 16, 17, 21, 18, 22, 23, 16, 19, 24, 25, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Binary weight is given by A000120.
a(2^k) = k+1 for any k>=0.
a(2^k-1) = 1 for any k>0.
a(A057168(k)) = a(k)+1 for any k>0.
a(A036563(k+1)) = k for any k>0.
Ordinal transform of A000120. - Alois P. Heinz, Dec 23 2018
LINKS
FORMULA
a(n) = 1 + A068076(n). - Antti Karttunen, May 22 2017
EXAMPLE
The numbers with binary weight 3 are: 7, 11, 13, 14, 19, ...
Hence: a(7)=1, a(11)=2, a(13)=3, a(14)=4, a(19)=5, ...
And more generally: a(A014311(k))=k for any k>0.
MAPLE
a:= proc() option remember; local a, b, t; b, a:=
proc() 0 end, proc(n) option remember; a(n-1);
t:= add(i, i=convert(n, base, 2)); b(t):= b(t)+1
end; a(0):=0; a
end():
seq(a(n), n=1..120); # Alois P. Heinz, Dec 23 2018
PROG
(Perl) See Links section.
(Haskell)
import Data.IntMap (empty, findWithDefault, insert)
a263017 n = a263017_list !! (n-1)
a263017_list = f 1 empty where
f x m = y : f (x + 1) (insert h (y + 1) m) where
y = findWithDefault 1 h m
h = a000120 x
-- Reinhard Zumkeller, Oct 09 2015
(Python)
def a(n):
x=bin(n)[2:].count("1")
return sum([1 for i in range(n) if bin(i)[2:].count("1")==x]) # Indranil Ghosh, May 24 2017
(Python)
from math import comb
def A263017(n):
c, k = 1, 0
for i, j in enumerate(bin(n)[-1:1:-1]):
if j == '1':
k += 1
c += comb(i, k)
return c # Chai Wah Wu, Mar 01 2023
CROSSREFS
One more than A068076.
Sequence in context: A336161 A336160 A335421 * A245328 A060162 A026730
KEYWORD
nonn,look,base
AUTHOR
Paul Tek, Oct 07 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)