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A360982
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Order the nonnegative integers by increasing binary length of values, then by decreasing binary length of values squared, then by increasing binary length of values cubed, etc.
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3
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0, 1, 3, 2, 6, 7, 5, 4, 12, 15, 14, 13, 10, 9, 8, 11, 23, 24, 25, 27, 30, 31, 29, 28, 26, 20, 18, 17, 16, 19, 21, 22, 46, 47, 48, 50, 49, 54, 55, 59, 60, 61, 63, 62, 58, 56, 57, 52, 51, 53, 39, 40, 36, 35, 34, 32, 33, 37, 38, 42, 41, 43, 44, 45, 91, 92, 93, 94
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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We ignore leading zeros (and 0 is assumed to have binary length 0).
This sequence is a permutation of the nonnegative integers with inverse A360983.
The order of appearance of two distinct integers, say x and y with x > y, depends on the parity of A360963(x, y): even implies x appears before y, odd implies x appears after y.
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LINKS
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EXAMPLE
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The first terms, alongside the binary length of their first powers, are:
n a(n) w1 w2 w3 w4 w5 w6
-- ---- -- -- -- -- -- --
0 0 0
1 1 1
2 3 2 4
3 2 2 3
4 6 3 6 8
5 7 3 6 9
6 5 3 5 7 10
7 4 3 5 7 9
8 12 4 8 11
9 15 4 8 12 16 20 24
10 14 4 8 12 16 20 23
11 13 4 8 12 15
12 10 4 7 10 14
13 9 4 7 10 13 16 20
14 8 4 7 10 13 16 19
15 11 4 7 11
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A360959 for a similar sequence.
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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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