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.

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

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-François Alcover, Mar 05 2016, adapted from Maple *)

Crossrefs

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

Sequence in context: A275896 A340754 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