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

Author

N. J. A. Sloane and Mira Bernstein

Keywords

• nonn
• base

References

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

Links

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

Crossrefs

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

Programs

Haskell

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

Mathematica

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

Python

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

Formula

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