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

Author

Paul D. Hanna and Antti Karttunen, Feb 21 2006

Keywords

• nonn

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

Crossrefs

Cf. Bisection of A116626. Complement of A116625?

Cf. A003987, A116624, A116628.

Cf. A235262

Programs

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 *)