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A359508 a(n) = log_2(A359507(n) - 1).

%I A359508 #22 Mar 08 2025 17:20:29
%S A359508 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 A359508 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 A359508 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 A359508 a(n) = log_2(A359507(n) - 1).
%C A359508 Conjecture: A359507(n) is always of the form 2^m + 1.
%C A359508 If log_2(A359507(n) - 1) is not an integer, then define a(n) = -1.
%H A359508 Antti Karttunen, <a href="/A359508/b359508.txt">Table of n, a(n) for n = 1..65537</a>
%F A359508 a(n) = A000523(A359507(n)-1).
%F A359508 Conjecture:
%F A359508 a(4k)   = 1 for k > 0,
%F A359508 a(4k+1) = 2 for k > 0,
%F A359508 a(4k+2) = 1 for k > 0,
%F A359508 a(4k+3) = a(k) + 2 for k > 0.
%F A359508 Apparently, a(n) = abs(A378218(1+n)). [This holds at least up to n=65537] - _Antti Karttunen_, Nov 22 2024
%F A359508 a(n) = A007814((n - 3*b(n + 1) + 2) mod b(n + 1) + b(n + 2) - 1) + 1, where b(n) = 2^A000523(A002264(n)) for n >= 4. - _Alan Michael Gómez Calderón_, Feb 25 2025
%o A359508 (PARI)
%o A359508 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 A359508 A359507(n) = (A359506(n)-n);
%o A359508 A359508(n) = (#digits(A359507(n)-1, 2)-1); \\ _Antti Karttunen_, Nov 22 2024
%Y A359508 Cf. A000523, A359506, A359507, A378218.
%K A359508 nonn
%O A359508 1,5
%A A359508 _Peter Kagey_, Jan 03 2023
%E A359508 More terms from _Antti Karttunen_, Nov 22 2024