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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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7
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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
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OFFSET
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0,2
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COMMENTS
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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 "nonattacking 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 chessboard (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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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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MATHEMATICA
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HalveDigit[d_, b_ /; OddQ[b] && b >= 3] /; 0 <= d <= b - 1 := Module[{x}, x /. Solve[2*x == d, x, Modulus -> b][[1]]];
HalveDigits[n_, b_] := Sum[b^i*HalveDigit[Mod[Floor[n/b^i] , b], b], {i, 0, Floor[Log[b, n + 1]]}];
QuintalQueens0Inv[n_] := HalveDigits[n, 5];
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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