A339451 Gray-code-like sequence in which, at each step, the least significant bit that has never been toggled from the previous value, is toggled.

0, 1, 0, 2, 3, 2, 0, 4, 5, 4, 6, 7, 6, 4, 0, 8, 9, 8, 10, 11, 10, 8, 12, 13, 12, 14, 15, 14, 12, 8, 0, 16, 17, 16, 18, 19, 18, 16, 20, 21, 20, 22, 23, 22, 20, 16, 24, 25, 24, 26, 27, 26, 24, 28, 29, 28, 30, 31, 30, 28, 24, 16, 0, 32, 33, 32, 34, 35, 34, 32, 36

Offset: 0

Author

Allan C. Wechsler, Dec 05 2020

Keywords

• easy
• nonn

Comments

Conjectured connections: the position of the bit that is toggled to derive a(n) from a(n-1) is A215020(n); the sequence of absolute differences of this sequence is A182105; there is some underlying connection to the "skew binary" counting system.

Examples

			For n = 18, a(n-1) = 8. That is the second 8 in the sequence. We cannot toggle the 1-bit, because that was already used to derive a(16) = 9 from a(15) = 8, so instead we toggle the 2-bit, yielding a(n) = 10.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65535

Crossrefs

Cf. A182105, A215020.

Programs

Maple

a:= proc() local b, a; b:= proc() 1/2 end; a:= proc(n)
      option remember; local h; if n=0 then 0 else h:=
      a(n-1); b(h):= 2*b(h); Bits[Xor](h, b(h)) fi end
    end():
seq(a(n), n=0..127);  # Alois P. Heinz, Dec 05 2020

Mathematica

a[m_] := Module[{b, a}, b[] = 1/2; a[n] := a[n] =
     Module[{h}, If[n == 0 ,  0 ,  h = a[n - 1];
     b[h] = 2*b[h]; BitXor[h, b[h]]]]; a[m]];
Table[a[n], {n, 0, 127}] (* Jean-François Alcover, May 15 2022, after Alois P. Heinz *)