A163252 a(0) = 0, and a(n) is the least positive integer not occurring earlier in the sequence such that a(n-1) and a(n) differ in only one bit when written in binary.

0, 1, 3, 2, 6, 4, 5, 7, 15, 11, 9, 8, 10, 14, 12, 13, 29, 21, 17, 16, 18, 19, 23, 22, 20, 28, 24, 25, 27, 26, 30, 31, 63, 47, 39, 35, 33, 32, 34, 38, 36, 37, 45, 41, 40, 42, 43, 59, 51, 49, 48, 50, 54, 52, 53, 55, 119, 87, 71, 67, 65, 64, 66, 70, 68, 69, 77, 73, 72, 74, 75, 79, 78

Offset

0,3

Comments

Step from a(488) = 237 = 11101101_2 to a(489) = 749 = 1011101101_2 is the first case when one term is two binary digits longer than the previous. Considering the leading zeros, though, they still differ in only one bit. - Ivan Neretin, Jun 25 2015

Links

Paul Tek, Table of n, a(n) for n = 0..10000

Formula

From Alois P. Heinz, Feb 02 2023: (Start)

A101080(a(n),a(n+1)) = 1.

a(A360307(n)) = n = A360307(a(n)). (End)

Maple

N:= 10: # to get all terms before the first where a(n) >= 2^N
B:= Array(0..2^N-1):
B[0]:= 1:
a[0]:= 0:
L:= Vector([0$N]):
for n from 1 do
  cands:= select(t -> B[t[1]]=0, [seq(`if`(L[i]=0, [a[n-1]+2^(i-1), i], [a[n-1]-2^(i-1), i]), i=1..N)]);
  if nops(cands)=0 then break fi;
  j:= min[index](map(t->t[1], cands));
  a[n]:= cands[j][1];
  i:= cands[j][2];
  B[a[n]]:= 1;
  L[i]:= 1 - L[i];
od:
seq(a[i], i=0..n-1); # Robert Israel, Jun 25 2015

Mathematica

Nest[Append[#, Min[Complement[BitXor[#[[-1]], 2^Range[0, Floor[Log2[#[[-1]]]] + 2]], #]]] &, {0, 1}, 71] (* Ivan Neretin, Jun 25 2015 *)

Crossrefs

Cf. A003188, A101080, A360307 (inverse).

Sequence in context: A265896 A254054 A303767 * A340250 A303773 A303769

Adjacent sequences: A163249 A163250 A163251 * A163253 A163254 A163255

Keyword

nonn,base

Author

Keenan Pepper, Jul 23 2009

Status

approved