|
%I #15 Nov 15 2020 14:09:40
%S 0,1,2,3,4,7,6,5,8,9,10,11,12,13,22,21,16,25,18,19,20,15,14,23,24,17,
%T 26,27,28,29,30,31,34,33,32,35,36,37,38,39,40,67,66,49,76,63,64,65,48,
%U 43,70,75,52,79,54,55,56,57,58,61,60,59,62,45,46,47,42,41
%N Reverse each run of nonzero digits in ternary expansion of n and convert back to decimal.
%C This sequence is a self-inverse permutation of nonnegative integers.
%H Rémy Sigrist, <a href="/A321726/b321726.txt">Table of n, a(n) for n = 0..19683</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(3 * n) = 3 * a(n).
%e For n = 3497:
%e - the ternary representation of 3497 is "11210112",
%e - we replace "1121" by "1211" and "112" by "211" and obtain "12110211",
%e - hence a(3497) = 3991.
%t rernz[n_]:=FromDigits[Flatten[If[FreeQ[#,0],Reverse[#],#]&/@SplitBy[ IntegerDigits[ n,3],#!=0&]],3]; Array[rernz,70,0] (* _Harvey P. Dale_, Nov 15 2020 *)
%o (PARI) a(n, base=3) = my (d=digits(n*base, base), nz=0); for (i=1, #d, if (d[i], nz++, if (nz, for (j=1, floor(nz/2), [d[i-j],d[i-nz-1+j]] = [d[i-
%o nz-1+j],d[i-j]]); nz=0))); fromdigits(d, base)/base
%Y See A321464 for a similar sequence.
%K nonn,base,look
%O 0,3
%A _Rémy Sigrist_, Nov 17 2018
|
