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Search: id:A106485
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| A106485 |
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CGT-tree negating involution of nonnegative integers. |
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+0
5
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| 0, 2, 1, 3, 32, 34, 33, 35, 16, 18, 17, 19, 48, 50, 49, 51, 8, 10, 9, 11, 40, 42, 41, 43, 24, 26, 25, 27, 56, 58, 57, 59, 4, 6, 5, 7, 36, 38, 37, 39, 20, 22, 21, 23, 52, 54, 53, 55, 12, 14, 13, 15, 44, 46, 45, 47, 28, 30, 29, 31, 60, 62, 61, 63, 128, 130, 129, 131, 160, 162
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This involution negates game trees used in the combinatorial game theory, when they are encoded in the way explained in A106486.
Cycles are confined into ranges [a(n),a(n+1)[, where a(0)=0 and a(n+1)=2^(2*a(n)), i.e. the ranges are [0,0], [1,3], [4,255], [256,(2^512)-1], ...
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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PROGRAM
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(Scheme:) (define (A106485 n) (let loop ((n n) (i 0) (s 0)) (cond ((zero? n) s) ((odd? n) (loop (/ (- n 1) 2) (1+ i) (+ s (if (even? i) (expt 2 (+ 1 (* 2 (A106485 (/ i 2))))) (expt 2 (* 2 (A106485 (/ (- i 1) 2)))))))) (else (loop (/ n 2) (1+ i) s)))))
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CROSSREFS
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A057300 is a "shallow" version which just swaps the left and right options of the game tree, but does not reflect the subtrees themselves. Cf. A106486-A106487.
Sequence in context: A014015 A108353 A059333 this_sequence A126008 A096098 A096097
Adjacent sequences: A106482 A106483 A106484 this_sequence A106486 A106487 A106488
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), May 21 2005
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