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A065256 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. 6
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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?

LINKS

Table of n, a(n) for n=0..71.

Index entries for sequences that are permutations of the natural numbers

MAPLE

[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);

MATHEMATICA

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];

Table[QuintalQueens0Inv[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, Mar 05 2016, adapted from Maple *)

CROSSREFS

Inverse permutation: A004515. A065256[n] = A065258[n+1]-1. Cf. also A065187, A065189.

Sequence in context: A240058 A275896 A163359 * A016573 A191818 A055171

Adjacent sequences:  A065253 A065254 A065255 * A065257 A065258 A065259

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Oct 26 2001

EXTENSIONS

Edited by Charles R Greathouse IV, Nov 01 2009

STATUS

approved

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Last modified December 11 14:03 EST 2017. Contains 295884 sequences.