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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))) 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.)