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Search: id:A065256
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| A065256 |
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Quintal Queens permutation of N: halve or multiply by 3 (mod 5) each digit (0->0, 1->3, 2->1, 3->4, 4->2) of the base 5 representation of n. |
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+0
6
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| 0, 3, 1, 4, 2, 15, 18, 16, 19, 17, 5, 8, 6, 9, 7, 20, 23, 21, 24, 22, 10, 13, 11, 14, 12, 75, 78, 76, 79, 77, 90, 93, 91, 94, 92, 80, 83, 81, 84, 82, 95, 98, 96, 99, 97, 85, 88, 86, 89, 87, 25, 28, 26, 29, 27, 40, 43, 41, 44, 42, 30, 33, 31, 34, 32, 45, 48, 46, 49, 47, 35, 38
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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All the permutations A004515 and A065256-A065258 consist of the first fixed term ("Queen on the corner") plus infinitely many 4-cycles and they satisfy the "non-attacking queen condition" that p(i+d) <> p(i)+-d for all i and d >= 1.
The corresponding infinite permutation matrix is a scale-invariant fractal (Cf. A048647) and any subarray (5^i)x(5^i) (i >= 1) cut from its corner gives a solution to the case n=5^i of the n nonattacking queens on n X n chess-board (A000170). Is there any permutation of N which would give solutions to the queen problem with more frequent intervals than A000351 ?
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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MAPLE
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[seq(QuintalQueens0Inv(j), j=0..124)];
HalveDigit := (d, b) -> op(2, op(1, msolve(2*x=d, b))); # b should be an odd integer >= 3 and d should be in range [0, b-1].
HalveDigits := proc(n, b) local i; add((b^i)*HalveDigit((floor(n/(b^i)) mod b), b), i=0..floor(evalf(log[b](n+1)))+1); end;
QuintalQueens0Inv := n -> HalveDigits(n, 5);
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CROSSREFS
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Inverse permutation: A004515. A065256[n] = A065258[n+1]-1. Cf. also A065187, A065189.
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KEYWORD
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nonn,base,new
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AUTHOR
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Antti Karttunen Oct 26 2001
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EXTENSIONS
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Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 01 2009
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