A116624 a(1)=1; for n>1, a(n) = least positive integer not appearing earlier such that {a(k) | 1 <= k <= n} and {a(k) XOR a(k-1) | 1 <= k <= n} are disjoint sets of distinct numbers.

1, 2, 4, 8, 5, 10, 16, 7, 9, 17, 32, 11, 18, 33, 19, 35, 20, 34, 22, 40, 21, 41, 28, 36, 27, 64, 29, 38, 31, 37, 65, 30, 66, 39, 68, 42, 67, 44, 70, 45, 69, 128, 46, 72, 47, 77, 129, 71, 131, 73, 130, 74, 132, 75, 134, 79, 136, 80, 133, 81, 135, 84, 137, 82, 139, 85

Offset

1,2

Comments

Another way to define this: A116624(1) = 1; A116624(n) = the least positive integer i distinct from any of A116624(1..n-1) and A116625(1..n-2), such that also (i XOR A116624(n-1)) is not present in A116625(1..n-2) nor in A116624(1..n-1).

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Mathematica

a = {1}; used = {}; Do[k = 1; While[MemberQ[Join[a, used], k] || MemberQ[Join[a, used], r = BitXor[a[[-1]], k]], k++]; AppendTo[a, k]; AppendTo[used, r], {n, 2, 66}]; a (* Ivan Neretin, Mar 13 2017 *)

Prog

(MIT/GNU Scheme)
(define (A116624 n) (cond ((= 1 n) 1) (else (let outloop ((i 1)) (let ((k (A003987bi i (A116624 (- n 1))))) (let inloop ((j (- n 1))) (cond ((zero? j) i) ((= i (A116624 j)) (outloop (+ i 1))) ((= i (A116625 (- j 1))) (outloop (+ i 1))) ((= k (A116625 (- j 1))) (outloop (+ i 1))) ((= k (A116624 j)) (outloop (+ i 1))) (else (inloop (- j 1))))))))))

Crossrefs

Cf. Bisection of A116626. Complement of A116625?

Cf. A003987, A116624, A116628.

Cf. A235262

Sequence in context: A021893 A036117 A307357 * A366304 A361191 A248573

Adjacent sequences: A116621 A116622 A116623 * A116625 A116626 A116627

Keyword

nonn

Author

Paul D. Hanna and Antti Karttunen, Feb 21 2006

Status

approved