A084471 Change 0 to 00 in binary representation of n.

1, 4, 3, 16, 9, 12, 7, 64, 33, 36, 19, 48, 25, 28, 15, 256, 129, 132, 67, 144, 73, 76, 39, 192, 97, 100, 51, 112, 57, 60, 31, 1024, 513, 516, 259, 528, 265, 268, 135, 576, 289, 292, 147, 304, 153, 156, 79, 768, 385, 388, 195, 400, 201, 204, 103, 448, 225

Offset: 1

Author

Reinhard Zumkeller, May 27 2003

Keywords

• nonn
• look
• base

Comments

a(n) = n iff n = 2^k - 1, k>0.

A023416(a(n))=A023416(n)*2; A000120(a(n))=A000120(n);

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A084472(n)=A007088(a(n)), A084473, A038573.

Ordered terms are in A060142.

Column k=2 of A340666.

Cf. A088698, A175047. - Robert G. Wilson v, Dec 10 2009

Programs

Haskell

a084471 1 = 1
a084471 x = 2 * (2 - d) * a084471 x' + d  where (x',d) = divMod x 2
-- Reinhard Zumkeller, Jul 16 2012

Maple

a:= n-> Bits[Join](subs(0=[0$2][], Bits[Split](n))):
seq(a(n), n=1..60);  # Alois P. Heinz, Jan 15 2021

Mathematica

f[n_] := FromDigits[Flatten[IntegerDigits[n, 2] /. {0 -> {0, 0}}], 2]; Array[f, 60] (* Robert G. Wilson v, Dec 10 2009 *)

Formula

a(1)=1, a(2*k+1)=2*a(k)+1, a(2*k)=4*a(k).