A106485 CGT-tree negating involution of nonnegative integers.

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

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. A106486-A106487.

Sequence in context: A354196 A059333 A345761 * A126008 A096098 A096097

Adjacent sequences: A106482 A106483 A106484 * A106486 A106487 A106488

Keyword

nonn

Author

Antti Karttunen, May 21 2005

Status

approved