A190619 Binary expansions of odd numbers with a single zero in their binary expansion.

101, 1011, 1101, 10111, 11011, 11101, 101111, 110111, 111011, 111101, 1011111, 1101111, 1110111, 1111011, 1111101, 10111111, 11011111, 11101111, 11110111, 11111011, 11111101, 101111111, 110111111, 111011111, 111101111, 111110111, 111111011, 111111101, 1011111111, 1101111111, 1110111111, 1111011111, 1111101111, 1111110111, 1111111011, 1111111101

Offset: 1

Author

N. J. A. Sloane, May 14 2011

Keywords

• nonn
• base

Comments

a(n) = A007088(A190620(n)). [Reinhard Zumkeller, May 14 2011]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Programs

Haskell

a190619 n = a190619_list !! (n-1)
a190619_list = map read $ f 2 1 :: [Integer] where
  f m k
    | k < m - 1 = ((take k ones) ++ "0" ++ (take (m-k) ones)) : f m (k+1)
    | otherwise = ((take k ones) ++ "01") : f (m + 1) 1
  ones = repeat '1'
-- Reinhard Zumkeller, May 15 2011

Maple

f:=k->(10^k-1)/9; for n from 3 to 12 do for i from n-2 by -1 to 1 do j:=f(n)-10^i; lprint(j); od; od;

Python

from itertools import count, islice
def agen():
    for d in count(3):
        b = (10**d - 1)//9
        for i in range(2, d):
            yield b - 10**(d-i)
print(list(islice(agen(), 50))) # Michael S. Branicky, Oct 13 2022

Python

from math import isqrt, comb
def A190619(n): return (10**((a:=(isqrt(n<<3)+1>>1)+1)+1)-1)//9-10**(comb(a,2)-n+1) # Chai Wah Wu, Dec 18 2024