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

1,1

Links

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

Formula

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

Example

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.

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 *)

Prog

(Python)
for n in range(1777):
    a = 2*n & n
    if a==2:
        print(n, end=', ')
(PARI) is(n)=bitand(n, 2*n)==2 \\ Charles R Greathouse IV, Jun 18 2012

Crossrefs

Cf. A213370, A004198, A003714.

Sequence in context: A023265 A018557 A270528 * A085616 A138723 A099955

Adjacent sequences: A213537 A213538 A213539 * A213541 A213542 A213543

Keyword

nonn,base

Author

Alex Ratushnyak, Jun 14 2012

Status

approved