A213540 Numbers k such that k AND k*2 = 2, where AND is the bitwise AND operator.

3, 11, 19, 35, 43, 67, 75, 83, 131, 139, 147, 163, 171, 259, 267, 275, 291, 299, 323, 331, 339, 515, 523, 531, 547, 555, 579, 587, 595, 643, 651, 659, 675, 683, 1027, 1035, 1043, 1059, 1067, 1091, 1099, 1107, 1155, 1163, 1171, 1187, 1195, 1283, 1291, 1299, 1315

Offset: 1

Author

Alex Ratushnyak, Jun 14 2012

Keywords

• nonn
• base

Examples

			In binary, 19 is 10011, while 2 * 19 = 38 is of course 100110. Since 010011 AND 100110 = 000010 (in decimal, 2), 19 is in the sequence.
20 is not in the sequence, since 010100 AND 101000 = 000000.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A213370, A004198, A003714.

Programs

Maple

F:= combinat[fibonacci]:
b:= proc(n) local j;
      if n=0 then 0
    else for j from 2 while F(j+1)<=n do od;
         b(n-F(j))+2^(j-2)
      fi
    end:
a:= n-> 8*b(n-1)+3:
seq(a(n), n=1..60);  # Alois P. Heinz, Jun 17 2012

Mathematica

Select[Range[1024], BitAnd[#, 2#] == 2 &] (* Alonso del Arte, Jun 18 2012 *)

PARI

is(n)=bitand(n,2*n)==2 \\ Charles R Greathouse IV, Jun 18 2012

Python

for n in range(1777):
    a = 2*n & n
    if a==2:
        print(n, end=',')

Formula

a(n) = A003714(n-1)*8 + 3.