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A227987
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If the run lengths of the binary representation of n are [1+r_1, 1+r_2, 1+r_3, ..., 1+r_k], then those of a(n) are [1+(r_1), 1+(r_1 XOR r_2), 1+(r_1 XOR r_2 XOR r_3), ..., 1+(r_1 XOR ... XOR r_k)], where XOR denotes the XOR binary operator.
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2
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1, 2, 3, 4, 5, 12, 7, 8, 19, 10, 11, 6, 51, 56, 15, 16, 71, 76, 9, 20, 21, 44, 23, 48, 13, 204, 25, 112, 455, 240, 31, 32, 271, 568, 143, 38, 307, 18, 79, 40, 83, 42, 43, 22, 179, 184, 47, 24, 783, 26, 27, 102, 819, 50, 207, 14, 1807, 3640, 911, 120, 3855
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OFFSET
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1,2
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COMMENTS
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This is a permutation of the natural numbers with inverse permutation A225607.
The sequence (n, a(n), a(a(n)), a(a(a(n))),...) is periodic for any n.
The run lengths of the binary representation of a fixed point are of the form [1, 1,...,1, K] (any number of ones followed by any number).
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LINKS
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EXAMPLE
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For n=927:
(1) binary representation of n = "1110011111",
(2) run lengths of n = [1+2,1+1,1+4],
(3) run lengths of a(n) = [1+(2),1+(2 XOR 1),1+(2 XOR 1 XOR 4)]=[3,4,8],
(4) binary representation of a(n) = "111000011111111",
(5) a(n) = 28927.
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PROG
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(Perl) 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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