A084474 -id:A084474 - cp's OEIS frontend

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

Reinhard Zumkeller, May 27 2003

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

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

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

Column k=4 of A340666.

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

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

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

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

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).

A084472 Write n in binary and replace 0 with 00.

Original entry on oeis.org

1, 100, 11, 10000, 1001, 1100, 111, 1000000, 100001, 100100, 10011, 110000, 11001, 11100, 1111, 100000000, 10000001, 10000100, 1000011, 10010000, 1001001, 1001100, 100111, 11000000, 1100001, 1100100, 110011, 1110000

Offset: 1

Reinhard Zumkeller, May 27 2003

nonn

a(n)=A007088(A084471(n)).

Cf. A084474, A038585.

Table[FromDigits[Flatten[IntegerDigits[n,2]/.(0->{0,0})]],{n,30}] (* Harvey P. Dale, Aug 27 2019 *)

cp's OEIS Frontend

A084473 Replace 0 with 0000 in binary representation of n.

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