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Replace 0 with 0000 in binary representation of n.
4

%I #30 Dec 18 2021 08:06:24

%S 1,16,3,256,33,48,7,4096,513,528,67,768,97,112,15,65536,8193,8208,

%T 1027,8448,1057,1072,135,12288,1537,1552,195,1792,225,240,31,1048576,

%U 131073,131088,16387,131328,16417,16432,2055,135168,16897,16912,2115,17152,2145

%N Replace 0 with 0000 in binary representation of n.

%C a(n) = n iff n = 2^k - 1, k>0 (A000225). - _Bernard Schott_, Dec 18 2021

%H Reinhard Zumkeller, <a href="/A084473/b084473.txt">Table of n, a(n) for n = 1..8191</a>

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

%F a(n) = A084471(A084471(n)).

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

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

%F A000120(a(n)) = A000120(n).

%p a:= n-> Bits[Join](subs(0=[0$4][], Bits[Split](n))):

%p seq(a(n), n=1..49); # _Alois P. Heinz_, Jan 15 2021

%t a[n_] := FromDigits[IntegerDigits[n, 2] /. 0 -> Sequence@@{0,0,0,0}, 2];

%t Array[a, 50] (* _Jean-François Alcover_, Dec 16 2021 *)

%o (Haskell)

%o a084473 1 = 1

%o a084473 x = 2 * (if b == 1 then 1 else 8) * a084473 x' + b

%o where (x', b) = divMod x 2

%o -- _Reinhard Zumkeller_, Mar 31 2015

%o (Python)

%o def a(n): return int(bin(n)[2:].replace('0', '0000'), 2)

%o print([a(n) for n in range(1, 46)]) # _Michael S. Branicky_, Jan 15 2021

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

%Y Column k=4 of A340666.

%K nonn,base,look

%O 1,2

%A _Reinhard Zumkeller_, May 27 2003