A084471
Change 0 to 00 in binary representation of n.
Original entry on oeis.org
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
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a084471 1 = 1
a084471 x = 2 * (2 - d) * a084471 x' + d where (x',d) = divMod x 2
-- Reinhard Zumkeller, Jul 16 2012
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a:= n-> Bits[Join](subs(0=[0$2][], Bits[Split](n))):
seq(a(n), n=1..60); # Alois P. Heinz, Jan 15 2021
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f[n_] := FromDigits[Flatten[IntegerDigits[n, 2] /. {0 -> {0, 0}}], 2]; Array[f, 60] (* Robert G. Wilson v, Dec 10 2009 *)
A340666
A(n,k) is derived from n by replacing each 0 in its binary representation with a string of k 0's; square array A(n,k), n>=0, k>=0, read by antidiagonals.
Original entry on oeis.org
0, 0, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 4, 3, 1, 0, 1, 8, 3, 4, 3, 0, 1, 16, 3, 16, 5, 3, 0, 1, 32, 3, 64, 9, 6, 7, 0, 1, 64, 3, 256, 17, 12, 7, 1, 0, 1, 128, 3, 1024, 33, 24, 7, 8, 3, 0, 1, 256, 3, 4096, 65, 48, 7, 64, 9, 3, 0, 1, 512, 3, 16384, 129, 96, 7, 512, 33, 10, 7
Offset: 0
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, ...
3, 3, 3, 3, 3, 3, 3, 3, 3, ...
1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, ...
3, 5, 9, 17, 33, 65, 129, 257, 513, ...
3, 6, 12, 24, 48, 96, 192, 384, 768, ...
7, 7, 7, 7, 7, 7, 7, 7, 7, ...
1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, ...
...
Rows n=0..17, 19 give:
A000004,
A000012,
A000079,
A010701,
A000302,
A000051(k+1),
A007283,
A010727,
A001018,
A087289,
A007582(k+1),
A062709(k+2),
A164346,
A181565(k+1),
A005009,
A181404(k+3),
A001025,
A199493,
A253208(k+1).
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A:= (n, k)-> Bits[Join](subs(0=[0$k][], Bits[Split](n))):
seq(seq(A(n, d-n), n=0..d), d=0..12);
# second Maple program:
A:= proc(n, k) option remember; `if`(n<2, n,
`if`(irem(n, 2, 'r')=1, A(r, k)*2+1, A(r, k)*2^k))
end:
seq(seq(A(n, d-n), n=0..d), d=0..12);
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A[n_, k_] := FromDigits[IntegerDigits[n, 2] /. 0 -> Sequence @@ Table[0, {k}], 2];
Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 02 2021 *)
A084474
Write n in binary and replace 0 with 0000.
Original entry on oeis.org
1, 10000, 11, 100000000, 100001, 110000, 111, 1000000000000, 1000000001, 1000010000, 1000011, 1100000000, 1100001, 1110000, 1111, 10000000000000000, 10000000000001, 10000000010000, 10000000011, 10000100000000
Offset: 1
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Table[FromDigits[Flatten[IntegerDigits[n,2]/.{0->{0,0,0,0}}]],{n,20}] (* Harvey P. Dale, Feb 19 2013 *)
Showing 1-3 of 3 results.
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