A116626 - OEIS

A116626

a(1)=1; a(odd n) = a(n-1) XOR a(n-2), for a(even n) we find the first i > 1 such that neither i nor (i XOR A116626(n-1)) is present in A116626(1..n-1), in which case a(n) = (i XOR A116626(n-1)).

1, 3, 2, 6, 4, 12, 8, 13, 5, 15, 10, 26, 16, 23, 7, 14, 9, 24, 17, 49, 32, 43, 11, 25, 18, 51, 33, 50, 19, 48, 35, 55, 20, 54, 34, 52, 22, 62, 40, 61, 21, 60, 41, 53, 28, 56, 36, 63, 27, 91, 64, 93, 29, 59, 38, 57, 31, 58, 37, 100, 65, 95, 30, 92, 66, 101, 39, 99, 68, 110, 42

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OFFSET

1,2

COMMENTS

This is a permutation of the natural numbers provided that A116625 is the complement of A116624. XOR is A003987.

LINKS

Table of n, a(n) for n=1..71.

Index entries for sequences that are permutations of the natural numbers

PROG

(MIT/GNU Scheme)

(define (A116626 n) (cond ((= 1 n) 1) ((odd? n) (A003987bi (A116626 (-1+ n)) (A116626 (- n 2)))) (else (let outloop ((i (A116648 (-1+ n)))) (let ((k (A003987bi i (A116626 (-1+ n))))) (let inloop ((j (- n 1))) (cond ((zero? j) k) ((= i (A116626 j)) (outloop (+ i 1))) ((= k (A116626 j)) (outloop (+ i 1))) (else (inloop (- j 1))))))))))

CROSSREFS

Cf. a(2n) = a(2n-1) XOR a(2n+1), a(2n+1) = A116624(n+1). Inverse: A116627. Bisections: A116624, A116625. Cf. A116648.

Sequence in context: A092401 A222208 A302853 * A074323 A162255 A164073

Adjacent sequences: A116623 A116624 A116625 * A116627 A116628 A116629

KEYWORD

nonn

AUTHOR

Paul D. Hanna and Antti Karttunen, Feb 21 2006

STATUS

approved