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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 2 18:52 EDT 2021. Contains 346428 sequences. (Running on oeis4.)