A304749 A303769 shown in binary.

0, 1, 11, 10, 110, 100, 101, 111, 1111, 1110, 1100, 1000, 1001, 1011, 1010, 11010, 11000, 10000, 10001, 10011, 10010, 10110, 10100, 10101, 10111, 11111, 11110, 11100, 11101, 11001, 11011, 111011, 111010, 111000, 110000, 100000, 100001, 100011, 100010, 100110, 100100, 100101, 100111, 101111, 101110, 101100, 101000, 101001, 101011, 101010, 1101010, 1101000

Offset

0,3

Links

Table of n, a(n) for n=0..51.

Index entries for sequences related to binary expansion of n

Formula

a(n) = A007088(A303769(n)).

Example

The code can be constructed by the rule: a(n+1) is either the largest number obtained from a(n) by toggling one 1-bit off if no such number is yet in the sequence, otherwise the least number not yet in sequence that can be obtained from a(n) by toggling one 0-bit on. In both cases the bit to be toggled is the rightmost possible that results yet an unencountered code. Note that this code doesn't cover all binary sequences, for example 1101 is missing:
   0       0
   1       1
   2      11
   3      10
   4     110
   5     100
   6     101
   7     111
   8    1111
   9    1110
  10    1100
  11    1000
  12    1001
  13    1011
  14    1010
  15   11010
  16   11000
  17   10000
  18   10001
  19   10011
  20   10010
  21   10110
  22   10100
  23   10101
  24   10111
  25   11111
  26   11110
  27   11100
  28   11101
  29   11001
  30   11011
  31  111011
  32  111010
  33  111000
  34  110000
  35  100000
  36  100001
  37  100011
  38  100010
  39  100110
  40  100100
  41  100101
  42  100111
  43  101111
  44  101110
  45  101100
  46  101000
  47  101001
  48  101011
  49  101010
  50 1101010
  51 1101000
  52 1100000
  53 1000000

Crossrefs

Cf. A007088, A303769.

Cf. also A304747.

Sequence in context: A106411 A353728 A304747 * A105028 A331560 A014550

Adjacent sequences: A304746 A304747 A304748 * A304750 A304751 A304752

Keyword

nonn,base

Author

Antti Karttunen, May 23 2018

Status

approved