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A084473 Replace 0 with 0000 in binary representation of n.

%I A084473 #30 Dec 18 2021 08:06:24
%S A084473 1,16,3,256,33,48,7,4096,513,528,67,768,97,112,15,65536,8193,8208,
%T A084473 1027,8448,1057,1072,135,12288,1537,1552,195,1792,225,240,31,1048576,
%U A084473 131073,131088,16387,131328,16417,16432,2055,135168,16897,16912,2115,17152,2145
%N A084473 Replace 0 with 0000 in binary representation of n.
%C A084473 a(n) = n iff n = 2^k - 1, k>0 (A000225). - _Bernard Schott_, Dec 18 2021
%H A084473 Reinhard Zumkeller, <a href="/A084473/b084473.txt">Table of n, a(n) for n = 1..8191</a>
%F A084473 a(1)=1, a(2*k+1)=2*a(k)+1, a(2*k)=16*a(k).
%F A084473 a(n) = A084471(A084471(n)).
%F A084473 A084474(n) = A007088(a(n));
%F A084473 A023416(a(n)) = A023416(n)*4.
%F A084473 A000120(a(n)) = A000120(n).
%p A084473 a:= n-> Bits[Join](subs(0=[0$4][], Bits[Split](n))):
%p A084473 seq(a(n), n=1..49);  # _Alois P. Heinz_, Jan 15 2021
%t A084473 a[n_] := FromDigits[IntegerDigits[n, 2] /. 0 -> Sequence@@{0,0,0,0}, 2];
%t A084473 Array[a, 50] (* _Jean-François Alcover_, Dec 16 2021 *)
%o A084473 (Haskell)
%o A084473 a084473 1 = 1
%o A084473 a084473 x = 2 * (if b == 1 then 1 else 8) * a084473 x' + b
%o A084473             where (x', b) = divMod x 2
%o A084473 -- _Reinhard Zumkeller_, Mar 31 2015
%o A084473 (Python)
%o A084473 def a(n): return int(bin(n)[2:].replace('0', '0000'), 2)
%o A084473 print([a(n) for n in range(1, 46)]) # _Michael S. Branicky_, Jan 15 2021
%Y A084473 Cf. A000120, A000225, A084471, A084474, A007088, A023416.
%Y A084473 Column k=4 of A340666.
%K A084473 nonn,base,look
%O A084473 1,2
%A A084473 _Reinhard Zumkeller_, May 27 2003