A340250 - OEIS

%I #39 Apr 25 2024 13:12:39

%S 0,1,3,2,6,4,5,7,15,11,9,13,12,8,10,14,30,22,18,26,24,16,20,28,29,21,

%T 17,25,27,19,23,31,63,47,39,55,51,35,43,59,57,41,33,49,53,37,45,61,60,

%U 44,36,52,48,32,40,56,58,42,34,50,54,38,46,62,126,94,78

%N Lexicographically earliest sequence of distinct nonnegative terms such that for any n >= 0, a(n+1) is obtained by inverting the leftmost binary digit (which is not a leading zero) in a(n) or if this is not possible by inverting the rightmost leading binary zero in a(n).

%C This sequence has similarities with A003188, where we invert the rightmost possible binary digit.

%C This sequence appears to be a permutation of the nonnegative integers.

%H Rémy Sigrist, <a href="/A340250/b340250.txt">Table of n, a(n) for n = 0..8191</a>

%H Rémy Sigrist, <a href="/A340250/a340250.gp.txt">PARI program for A340250</a>

%H Rémy Sigrist, <a href="/A340250/a340250.png">Binary plot of the sequence for n = 0..256</a>

%e The first terms, alongside their binary representation, are:

%e   n   a(n)  bin(a(n))

%e   --  ----  ---------

%e    0     0          0

%e    1     1          1

%e    2     3         11

%e    3     2         10

%e    4     6        110

%e    5     4        100

%e    6     5        101

%e    7     7        111

%e    8    15       1111

%e    9    11       1011

%e   10     9       1001

%e   11    13       1101

%e   12    12       1100

%e   13     8       1000

%e   14    10       1010

%e   15    14       1110

%o (PARI) \\ See Links section.

%Y Cf. A003188, A340251, A340253 (ternary analog), A340254 (decimal analog), A340255 (factorial base analog), A340256 (primorial base analog).

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Jan 02 2021