%I A065256
%S A065256 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,
%T A065256 78,76,79,77,90,93,91,94,92,80,83,81,84,82,95,98,96,99,97,85,88,86,89,
%U A065256 87,25,28,26,29,27,40,43,41,44,42,30,33,31,34,32,45,48,46,49,47,35,38
%N 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.
%C A065256 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.
%C A065256 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 ?
%H A065256 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%p A065256 [seq(QuintalQueens0Inv(j),j=0..124)];
%p A065256 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].
%p A065256 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;
%p A065256 QuintalQueens0Inv := n -> HalveDigits(n,5);
%Y A065256 Inverse permutation: A004515. A065256[n] = A065258[n+1]-1. Cf. also A065187, 
               A065189.
%Y A065256 Sequence in context: A115659 A068028 A163359 this_sequence A016573 A055171 
               A101038
%Y A065256 Adjacent sequences: A065253 A065254 A065255 this_sequence A065257 A065258 
               A065259
%K A065256 nonn,base
%O A065256 0,2
%A A065256 Antti Karttunen Oct 26 2001
%E A065256 Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 
               01 2009