A084473 Replace 0 with 0000 in binary representation of n.

1, 16, 3, 256, 33, 48, 7, 4096, 513, 528, 67, 768, 97, 112, 15, 65536, 8193, 8208, 1027, 8448, 1057, 1072, 135, 12288, 1537, 1552, 195, 1792, 225, 240, 31, 1048576, 131073, 131088, 16387, 131328, 16417, 16432, 2055, 135168, 16897, 16912, 2115, 17152, 2145

Offset: 1

Author

Reinhard Zumkeller, May 27 2003

Keywords

• nonn
• base
• look

Comments

a(n) = n iff n = 2^k - 1, k>0 (A000225). - Bernard Schott, Dec 18 2021

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..8191

Crossrefs

Cf. A000120, A000225, A084471, A084474, A007088, A023416.

Column k=4 of A340666.

Programs

Haskell

a084473 1 = 1
a084473 x = 2 * (if b == 1 then 1 else 8) * a084473 x' + b
            where (x', b) = divMod x 2
-- Reinhard Zumkeller, Mar 31 2015

Maple

a:= n-> Bits[Join](subs(0=[0$4][], Bits[Split](n))):
seq(a(n), n=1..49);  # Alois P. Heinz, Jan 15 2021

Mathematica

a[n_] := FromDigits[IntegerDigits[n, 2] /. 0 -> Sequence@@{0,0,0,0}, 2];
Array[a, 50] (* Jean-François Alcover, Dec 16 2021 *)

Python

def a(n): return int(bin(n)[2:].replace('0', '0000'), 2)
print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Jan 15 2021

Formula

a(1)=1, a(2*k+1)=2*a(k)+1, a(2*k)=16*a(k).

a(n) = A084471(A084471(n)).

A084474(n) = A007088(a(n));

A023416(a(n)) = A023416(n)*4.

A000120(a(n)) = A000120(n).