A030306 -id:A030306 - cp's OEIS frontend

A003607 Location of 0's when natural numbers are listed in binary.

0, 3, 7, 8, 10, 14, 19, 20, 21, 23, 24, 27, 29, 31, 36, 37, 40, 45, 51, 52, 53, 54, 56, 57, 58, 61, 62, 64, 66, 67, 71, 73, 74, 76, 78, 81, 84, 86, 92, 93, 94, 97, 98, 102, 104, 107, 113, 114, 118, 124, 131, 132, 133, 134, 135, 137, 138, 139, 140, 143, 144

Offset: 0

N. J. A. Sloane and Mira Bernstein

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A030190, A030302, A030303, A030306, A056062.

import Data.List (elemIndices)
a003607 n = a003607_list !! n
a003607_list = elemIndices 0 a030190_list
-- Reinhard Zumkeller, Dec 11 2011

Position[IntegerDigits[Range[0, 100], 2] // Flatten, 0] - 1 // Flatten (* Jean-François Alcover, Oct 06 2016 *)

from itertools import count, islice
def A003607_gen(): # generator of terms
    return (i for i, s in enumerate(d for n in count(0) for d in bin(n)[2:]) if s == '0')
A003607_list = list(islice(A003607_gen(),30)) # Chai Wah Wu, Feb 18 2022

A030190(a(n)) = 0. [Reinhard Zumkeller, Dec 11 2011]

A056062 Run lengths in infinite binary Champernowne string (A030190) formed by concatenation of 0, 1, 2 ... in base 2.

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 1, 3, 1, 4, 3, 1, 2, 2, 1, 1, 1, 1, 1, 4, 2, 2, 1, 4, 1, 5, 4, 1, 3, 2, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 5, 3, 2, 2, 3, 1, 1, 1, 2, 1, 5, 2, 3, 1, 5, 1, 6, 5, 1, 4, 2, 3, 1, 1, 1, 3, 3, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 4, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Helge Robitzsch (hrobi(AT)math.uni-goettingen.de), Jul 27 2000

			The string starts with 011011100101110111... (concatenation of 0, 1, 10, 11, 100, 101, 110, 111, ...) so initial runs are 1, 2, 1, 3, ...

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A030190, A003607, A030306, A318924.

import Data.List (group)
a056062 n = a056062_list !! n
a056062_list = map length $ group a030190_list
-- Reinhard Zumkeller, Mar 26 2013

Length /@ (Split@(Join @@ Table[ IntegerDigits[i, 2], {i, 0, 100}]))  (*  Olivier Gérard, Mar 27 2011 *)
Length/@Split[Flatten[IntegerDigits[Range[0,50],2]]] (* Harvey P. Dale, May 24 2015 *)

Edited by Charles R Greathouse IV, Apr 26 2010

Data corrected for n > 44 by Reinhard Zumkeller, Mar 26 2013

cp's OEIS Frontend

A003607 Location of 0's when natural numbers are listed in binary.

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