A003607 Location of 0's when natural numbers are listed in binary. (Formerly M2612)

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

0,2

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A089970 A019270 A047357 * A087859 A300082 A050010

Adjacent sequences: A003604 A003605 A003606 * A003608 A003609 A003610

Keyword

nonn,base

Author

N. J. A. Sloane and Mira Bernstein

Status

approved