A319268 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the binary representation of n^2 starts with the binary representation of a(n).

1, 2, 4, 8, 3, 9, 6, 16, 5, 12, 7, 18, 10, 24, 14, 32, 36, 20, 11, 25, 13, 15, 33, 72, 19, 21, 22, 49, 26, 28, 30, 64, 17, 144, 38, 40, 42, 45, 23, 50, 52, 27, 57, 60, 31, 66, 34, 288, 37, 39, 81, 84, 43, 91, 47, 98, 101, 105, 54, 56, 29, 120, 62, 128, 132, 68

Offset

1,2

Comments

This sequence is a permutation of the natural numbers with inverse A319499.

We can build a variant of this sequence for any base b > 1.

We can build a variant of this sequence for any strictly increasing sequence of nonnegative integers.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A319268

Rémy Sigrist, Colored logarithmic scatterplot of the first 10000 terms (where the color is function of A070939(n^2) - A070939(a(n)))

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the binary representation of n^2 with a(n) in parentheses, are:
  n   a(n)  bin(n^2)
  --  ----  --------
   1     1          (1)
   2     2        (10)0
   3     4       (100)1
   4     8      (1000)0
   5     3      (11)001
   6     9     (1001)00
   7     6     (110)001
   8    16    (10000)00
   9     5    (101)0001
  10    12    (1100)100
  11     7    (111)1001
  12    18   (10010)000
  13    10   (1010)1001
  14    24   (11000)100
  15    14   (1110)0001
  16    32  (100000)000
  17    36  (100100)001
  18    20  (10100)0100
  19    11  (1011)01001
  20    25  (11001)0000

Mathematica

a = {1}; Do[r = IntegerDigits[n^2, 2]; AppendTo[a, Min@Complement[Table[FromDigits[Take[r, k], 2], {k, Length@r}], a]], {n, 2, 66}]; a (* Ivan Neretin, Oct 24 2018 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A000290, A070939, A272679, A319499.

Sequence in context: A197382 A332521 A246363 * A277272 A109588 A254788

Adjacent sequences: A319265 A319266 A319267 * A319269 A319270 A319271

Keyword

nonn,base

Author

Rémy Sigrist, Sep 16 2018

Status

approved