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A057300
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Binary counter with odd/even bit positions swapped; base 4 counter with 1's replaced by 2's and vice versa.
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14
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0, 2, 1, 3, 8, 10, 9, 11, 4, 6, 5, 7, 12, 14, 13, 15, 32, 34, 33, 35, 40, 42, 41, 43, 36, 38, 37, 39, 44, 46, 45, 47, 16, 18, 17, 19, 24, 26, 25, 27, 20, 22, 21, 23, 28, 30, 29, 31, 48, 50, 49, 51, 56, 58, 57, 59, 52, 54, 53, 55, 60, 62, 61, 63, 128, 130, 129, 131, 136, 138
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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A self-inverse permutation of the integers
It is not true in general that a(2n) = -2a(n) + 5n, a(2n+1) = -2a(n) + 5n + 2 as was originally conjectured.
Counterexamples: a(46) = 29; a(92) = 172; binary(172) = [1, 0, 1, 0, 1, 1, 0, 0], but binary(-2*29+5*92) = binary(402) = [1, 1, 0, 0, 1, 0, 0, 1, 0]. a(45) = 30; a(91) = 167; binary(167) = [1, 0, 1, 0, 0, 1, 1, 1], but -2*30+5*91+2=397 and binary(397) = [1, 1, 0, 0, 0, 1, 1, 0, 1] - Lambert Herrgesell (zero815(AT)googlemail.com), Jan 13 2007
a(n) = n if and only if n can be written as 3*Sum[d_i*4^k, 0 <= k < infinity], where d_i is either 0 or 1. - Jon Perry, Oct 06 2012
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LINKS
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Table of n, a(n) for n=0..69.
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(4n+k) = 4a(n) + a(k), 0 <= k <= 3. - Jon Perry, Oct 06 2012
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EXAMPLE
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a(31) = a(4*7+3) = 4*a(7) + a(3) = 4*11 + 3 = 47.
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CROSSREFS
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Cf. A057301.
Sequence in context: A078045 A202624 A145490 * A076655 A101486 A086606
Adjacent sequences: A057297 A057298 A057299 * A057301 A057302 A057303
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KEYWORD
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easy,nonn
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AUTHOR
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Marc LeBrun, Aug 24 2000
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STATUS
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approved
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