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A319268
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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).
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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