OFFSET
0,5
COMMENTS
a(n) has a 01 bit pair in place of each 10 bit pair in n, and everywhere else 0 bits. Or equivalently a(n) has a 1-bit immediately below each run of 1's in n, but excluding a run ending at the least significant bit since below that is below the radix point. - Kevin Ryde, Feb 27 2021
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..8191
FORMULA
a(n) = (n XOR floor(n/2)) AND floor(n/2) = (n AND floor(n/2)) XOR floor(n/2).
a(n) = floor(n/2) AND NOT n. - Chai Wah Wu, Jun 29 2022
EXAMPLE
From Kevin Ryde, Feb 27 2021: (Start)
n = 7267 = binary 1110001100011
a(n) = 528 = binary 01000010000 1-bit below each run
(End)
PROG
(Python)
for n in range(333): print (n ^ (n>>1)) & (n>>1),
(Python)
def A229762(n): return ~n& n>>1 # Chai Wah Wu, Jun 29 2022
(Haskell)
import Data.Bits ((.&.), xor, shiftR)
a229762 n = (n `xor` shiftR n 1) .&. shiftR n 1 :: Int
-- Reinhard Zumkeller, Oct 10 2013
(PARI) a(n) = bitnegimply(n>>1, n); \\ Kevin Ryde, Feb 27 2021
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Alex Ratushnyak, Sep 28 2013
STATUS
approved