A342892 a(n) is the complement of the bit two places to the left of the least significant "1" in the binary expansion of n.

1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0

Offset

0

Links

Michael De Vlieger, Table of n, a(n) for n = 0..16384

Example

The bit to be complemented is in (parens).
n = 13 = 1(1)01_2, so a(13) = 0.
n = 12 = 1100_2 = (0)1100_2 so a(12) = complement of initial 0 = 1.

Maple

a342892 := proc(n) local p, s1, s2, i;
if n=0 then return(1); fi;
s1:=convert(n, base, 2); s2:=nops(s1);
for i from 1 to s2 do if s1[i]=1 then p:=i; break; fi; od:
if p <= s2-2 then 1-s1[p+2]; else 1; fi; end;
[seq(a342892(i), i=0..120)];
# second Maple program:
a:= n-> 1-irem(iquo(n/2^padic[ordp](n, 2), 4), 2):
seq(a(n), n=0..120);  # Alois P. Heinz, Apr 08 2021

Mathematica

{0}~Join~Array[If[#2 < 1, 1, #1[[#2]] /. {0 -> 1, 1 -> 0}] & @@ {#, Position[#, 1][[-1, 1]] - 2} &[IntegerDigits[#, 2]] &, 104] (* Michael De Vlieger, Apr 08 2021 *)

Prog

(Python)
def A342892(n):
    s = bin(n)[2:]
    m = len(s)
    i = s[::-1].find('1')
    return 1-int(s[m-i-3]) if m-i-3 >= 0 else 1 # Chai Wah Wu, Apr 08 2021

Crossrefs

If we change "two places" to "one place" we get A014577.

Sequence in context: A114592 A344864 A140653 * A071036 A071038 A131522

Adjacent sequences: A342889 A342890 A342891 * A342893 A342894 A342895

Keyword

nonn

Author

N. J. A. Sloane, Apr 08 2021.

Status

approved