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A195467
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Consecutive powers of the Gray code permutation.
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3
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0, 1, 0, 1, 2, 3, 0, 1, 3, 2, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 0, 1, 2, 3, 5, 4, 7, 6, 10, 11, 8, 9, 15, 14, 13, 12, 0, 1, 3, 2, 7, 6, 4, 5, 15, 14, 12, 13, 8, 9, 11, 10
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OFFSET
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0,5
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COMMENTS
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The powers of the Gray code permutation (GCP, A003188) form an infinite array, where row n is the n-th power of the GCP. Row 0 is the identity permutation (i.e., the sequence of nonnegative integers), and row 1 is the GCP itself.
The different powers of the n-bit GCP form a matrix of size (A062383(n-1)) X (2^n).
This sequence represents the infinite array in a somewhat redundant way: It shows the rows of all the (2^n) X (2^2^n) matrices of powers of (2^n)-bit GCP. So this sequence forms a triangle, and these 3 matrices are its first 7 rows:
The 1-bit GCP is the identity permutation:
0: 0 1
The 2 different powers of the 2-bit GCP:
0: 0 1 2 3
1: 0 1 3 2
The 4 different powers of the 4-bit GCP:
0: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1: 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8
2: 0 1 2 3 5 4 7 6 10 11 8 9 15 14 13 12
3: 0 1 3 2 7 6 4 5 15 14 12 13 8 9 11 10
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This array A can be defined using the binary array B = A197819 by
A = B + 2 * 2stretched(B) + 4 * 4stretched(B) + 8 * 8stretched(B) + ...
where nstretched has the following meaning:
2stretched(1,2,3,4,...) = 1,1,2,2,3,3,4,4,...
4stretched(1,2,3,4,...) = 1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,...
etc.
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LINKS
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CROSSREFS
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Cf. A003188 (Gray code permutation).
Cf. A006068 (inverse of the Gray code permutation).
Cf. A064706 (square of the Gray code permutation).
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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