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A337909
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Distinct terms of A080079 in the order in which they appear.
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1
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1, 2, 4, 3, 8, 7, 6, 5, 16, 15, 14, 13, 12, 11, 10, 9, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 128
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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 positive integers.
The cardinality of {2^k, ..., (2^k - 0^k)/2 + 1} is A011782(k).
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LINKS
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FORMULA
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a(1) = 1 and a(n) = A080079(n - 1 + 2^floor(log_2(n - 1))) if n > 1.
a(n) = 3*A053644(n-1) - (n-1), if n > 1.
a(n) = A280510(n) - n + 1, if n > 1. (End)
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EXAMPLE
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(2^0, ..., (2^0 - 0^0)/2 + 1) = (1),
(2^1, ..., (2^1 - 0^1)/2 + 1) = (2),
(2^2, ..., (2^2 - 0^2)/2 + 1) = (4, 3),
(2^3, ..., (2^3 - 0^3)/2 + 1) = (8, 7, 6, 5)...
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MATHEMATICA
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{1}~Join~Array[3*2^(IntegerLength[# - 1, 2] - 1) - # + 1 &, 64, 2] (* Michael De Vlieger, Oct 05 2020 *)
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PROG
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(PARI) a(n) = if(n--, 3<<logint(n, 2) - n, 1); \\ Kevin Ryde, Sep 29 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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