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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.
1
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
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
Sequence in context: A307688 A056888 A286297 * A111182 A178142 A375751
KEYWORD
easy,nonn
AUTHOR
Allan C. Wechsler, Dec 05 2020
STATUS
approved