

A106485


CGTtree negating involution of nonnegative integers.


5



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
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OFFSET

0,2


COMMENTS

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], ...


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..1023
Index entries for sequences that are permutations of the natural numbers


PROG

(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)))))


CROSSREFS

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. A106486A106487.
Sequence in context: A014015 A108353 A059333 * A126008 A096098 A096097
Adjacent sequences: A106482 A106483 A106484 * A106486 A106487 A106488


KEYWORD

nonn


AUTHOR

Antti Karttunen, May 21 2005


STATUS

approved



