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 A359507 #13 Nov 23 2024 00:29:26 %S A359507 0,2,3,3,3,5,3,5,3,5,3,9,3,5,3,9,3,5,3,9,3,5,3,17,3,5,3,9,3,5,3,17,3, %T A359507 5,3,9,3,5,3,17,3,5,3,9,3,5,3,33,3,5,3,9,3,5,3,17,3,5,3,9,3,5,3,33,3, %U A359507 5,3,9,3,5,3,17,3,5,3,9,3,5,3,33,3,5,3,9,3,5,3,17,3,5,3,9,3,5,3,65,3,5,3,9,3,5 %N A359507 a(n) is the least integer k such that there exists a strictly increasing integer sequence n = b_1 < b_2 < ... < b_t = n + k with the property that b_1 XOR b_2 XOR ... XOR b_t = 0. %C A359507 Conjecture: a(n) is of the form 2^k + 1 for all n > 0. %H A359507 Antti Karttunen, <a href="/A359507/b359507.txt">Table of n, a(n) for n = 0..65537</a> %F A359507 a(n) = A359506(n) - n. %o A359507 (PARI) %o A359507 A359506(n) = if(n==0, return (0), my (x=[n], y); for (m=n+1, oo, if (vecmin(y=[bitxor(v, m) | v<-x])==0, return (m), x=setunion(x, Set(y))))); \\ From A359506. %o A359507 A359507(n) = (A359506(n)-n); \\ _Antti Karttunen_, Nov 22 2024 %Y A359507 Cf. A092487, A359506, A359508. %K A359507 nonn %O A359507 0,2 %A A359507 _Peter Kagey_, Jan 03 2023 %E A359507 More terms from _Antti Karttunen_, Nov 22 2024