Voozh

A056539

Self-inverse permutation: reverse the bits in binary expansion of n and also complement them (0->1, 1->0) if the run count (A005811) is even.

0, 1, 2, 3, 6, 5, 4, 7, 14, 9, 10, 13, 12, 11, 8, 15, 30, 17, 22, 25, 26, 21, 18, 29, 28, 19, 20, 27, 24, 23, 16, 31, 62, 33, 46, 49, 54, 41, 38, 57, 58, 37, 42, 53, 50, 45, 34, 61, 60, 35, 44, 51, 52, 43, 36, 59, 56, 39, 40, 55, 48, 47, 32, 63, 126, 65, 94, 97, 110, 81, 78

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Paul Tek, Table of n, a(n) for n = 0..8191

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(2n) = A036044(2n), a(2n+1) = A030101(2n+1). - Antti Karttunen, Feb 14 2003

EXAMPLE

n: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

binary expansion: 0, 1, 10, 11, 100, 101, 110, 111,1000,1001,1010,1011,1100,1101,1110,1111

reversed/complemented: 0, 1, 10, 11, 110, 101, 100, 111,1110,1001,1010,1101,1100,1011,1000,1111

MAPLE

[seq(runcounts2binexp(reverse(binexp2runcounts(j))), j=0..511)];

runcounts2binexp := proc(c) local i, e, n; n := 0; for i from 1 to nops(c) do e := c[i]; n := ((2^e)*n) + ((i mod 2)*((2^e)-1)); od; RETURN(n); end;

binexp2runcounts := proc(nn) local n, a, p, c; n := nn; a := []; p := (`mod`(n, 2)); c := 0; while(n > 0) do c := c+1; n := floor(n/2); if((`mod`(n, 2)) <> p) then a := [c, op(a)]; c := 0; p := (`mod`(p+1, 2)); fi; od; RETURN(a); end;

# reverse given in A056538

MATHEMATICA

A056539[n_] := If[n == 0, 0, FromDigits[Reverse[If[Last[#] == 1, #, 1-#]], 2] & [IntegerDigits[n, 2]]];

Array[A056539, 100, 0] (* Paolo Xausa, Nov 28 2024 *)

PROG

(Python)

def a005811(n): return bin(n^(n>>1))[2:].count("1")

def a(n):

if n==0: return 0

x=bin(n)[2:][::-1]

if a005811(n)%2==1: return int(x, 2)

z=''.join('1' if i == '0' else '0' for i in x)