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

0,4

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A182105, A215020.

Sequence in context: A307688 A056888 A286297 * A111182 A178142 A076427

Adjacent sequences: A339448 A339449 A339450 * A339452 A339453 A339454

Keyword

easy,nonn

Author

Allan C. Wechsler, Dec 05 2020

Status

approved