This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A116624 #16 Dec 14 2023 15:36:55
%S A116624 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,
%T A116624 64,29,38,31,37,65,30,66,39,68,42,67,44,70,45,69,128,46,72,47,77,129,
%U A116624 71,131,73,130,74,132,75,134,79,136,80,133,81,135,84,137,82,139,85
%N 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.
%C A116624 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).
%H A116624 Ivan Neretin, <a href="/A116624/b116624.txt">Table of n, a(n) for n = 1..10000</a>
%t A116624 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 *)
%o A116624 (MIT/GNU Scheme)
%o A116624 (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))))))))))
%Y A116624 Cf. Bisection of A116626. Complement of A116625?
%Y A116624 Cf. A003987, A116624, A116628.
%Y A116624 Cf. A235262
%K A116624 nonn
%O A116624 1,2
%A A116624 _Paul D. Hanna_ and _Antti Karttunen_, Feb 21 2006