|
%I #14 Jan 20 2019 23:18:55
%S 0,1,4,3,2,9,12,7,16,5,36,19,6,25,28,15,8,33,20,11,18,73,76,39,48,13,
%T 100,51,14,57,60,31,64,17,132,67,10,41,44,23,144,37,292,147,38,153,
%U 156,79,24,97,52,27,50,201,204,103,112,29,228,115,30,121,124,63,32
%N Take the binary representation of n, increase each run of 0's by one 0 if the length of run is odd, otherwise, if length of run is even, remove one 0. a(n) is the decimal equivalent of the result.
%C This is a self-inverse permutation of the positive integers.
%H Rémy Sigrist, <a href="/A266150/b266150.txt">Table of n, a(n) for n = 0..8192</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e a(4) = 2 since 4 = 100 binary -> 10 = 2 decimal.
%e a(5) = 9 since 5 = 101 binary -> 1001 = 9 decimal.
%e a(6) = 12 since 6 = 110 binary -> 1100 = 12 decimal.
%t Table[FromDigits[#, 2] &@ Flatten[If[First@ # == 0, If[OddQ@ Length@ #, Append[IntegerDigits@ #, 0], Most@ IntegerDigits@ #], #] & /@ Split@ IntegerDigits[n, 2]], {n, 64}] (* _Michael De Vlieger_, Dec 22 2015 *)
%o (PARI) a(n) = if (n==0, 0, my (b=n%2, r=valuation(n+b, 2), rr=if (b, r, r%2, r+1, r-1)); (a(n\2^r)+b)*2^rr-b) \\ _Rémy Sigrist_, Jan 20 2019
%Y Cf. A007088, A084483, A162853, A175046, A175047, A175048, A266151.
%K nonn,base
%O 0,3
%A _Alex Ratushnyak_, Dec 21 2015
%E a(0) = 0 prepended by _Rémy Sigrist_, Jan 20 2019
|
