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A364954 The length of the common prefix in the binary expansions of A156552(n) and A156552(A163511(n)).

%I A364954 #8 Sep 02 2023 16:59:53
%S A364954 0,1,2,2,1,3,3,3,2,1,1,4,2,3,2,4,1,2,1,1,1,1,1,5,1,2,1,3,3,2,5,5,1,1,
%T A364954 1,2,1,1,1,1,1,1,1,1,1,1,1,6,1,1,2,2,2,1,2,3,3,3,3,2,4,5,3,6,1,1,1,1,
%U A364954 1,1,1,2,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,2,1,2,1,2,2,2,2,5
%N A364954 The length of the common prefix in the binary expansions of A156552(n) and A156552(A163511(n)).
%H A364954 Antti Karttunen, <a href="/A364954/b364954.txt">Table of n, a(n) for n = 1..65537</a>
%o A364954 (PARI)
%o A364954 Abincompreflen(n, m) = { my(x=binary(n), y=binary(m), u=min(#x, #y)); for(i=1, u, if(x[i]!=y[i], return(i-1))); (u); };
%o A364954 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
%o A364954 A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A364954 A364954(n) = Abincompreflen(A156552(n), A156552(A163511(n)));
%Y A364954 Cf. A156552, A163511, A364955.
%Y A364954 Cf. also A364569.
%K A364954 nonn
%O A364954 1,3
%A A364954 _Antti Karttunen_, Sep 02 2023