%I #14 Nov 22 2024 20:32:37

%S 0,1,1,1,2,1,2,1,2,1,3,1,2,1,3,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,4,1,2,1,

%T 3,1,2,1,4,1,2,1,3,1,2,1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,5,1,2,1,3,1,

%U 2,1,4,1,2,1,3,1,2,1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,6,1,2,1,3,1,2,1,4,1,2

%N a(n) = log_2(A359507(n) - 1).

%C Conjecture: A359507(n) is always of the form 2^m + 1.

%C If log_2(A359507(n) - 1) is not an integer, then define a(n) = -1.

%H Antti Karttunen, <a href="/A359508/b359508.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A000523(A359507(n)-1).

%F Conjecture:

%F a(1) = 0,

%F a(2) = 1,

%F a(3) = 1,

%F a(4k) = 1 for k > 0,

%F a(4k+1) = 2 for k > 0,

%F a(4k+2) = 1 for k > 0,

%F a(4k+3) = a(k) + 2 for k > 0.

%F Apparently, a(n) = abs(A378218(1+n)). [This holds at least up to n=65537] - _Antti Karttunen_, Nov 22 2024

%o (PARI)

%o 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(n) = (A359506(n)-n);

%o A359508(n) = (#digits(A359507(n)-1, 2)-1); \\ _Antti Karttunen_, Nov 22 2024

%Y Cf. A000523, A359506, A359507, A378218.

%K nonn,changed

%O 1,5

%A _Peter Kagey_, Jan 03 2023

%E More terms from _Antti Karttunen_, Nov 22 2024