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A374176 a(n) is the maximum number of consecutive bit changes in the binary representation of n.

%I A374176 #23 Jul 07 2024 17:39:32
%S A374176 0,1,0,1,2,1,0,1,1,3,2,1,2,1,0,1,1,2,1,3,4,2,2,1,1,3,2,1,2,1,0,1,1,2,
%T A374176 1,2,3,1,1,3,3,5,4,2,2,2,2,1,1,2,1,3,4,2,2,1,1,3,2,1,2,1,0,1,1,2,1,2,
%U A374176 3,1,1,2,2,4,3,1,2,1,1,3,3,3,3,5,6,4,4,2,2,3,2,2,2,2,2,1,1,2,1,2,3,1,1,3,3
%N A374176 a(n) is the maximum number of consecutive bit changes in the binary representation of n.
%H A374176 Hugo Pfoertner, <a href="/A374176/b374176.txt">Table of n, a(n) for n = 1..8192</a>
%F A374176 a(n) = A038374(A038554(n)), with A038374(0) = 0. - _Michael S. Branicky_, Jul 06 2024
%e A374176 a(1117) = 3:
%e A374176   1117_2 = [1 0 0 0 1 0 1 1 1 0 1]
%e A374176              ^     ^ ^ ^     ^ ^
%e A374176              1       3        2
%e A374176             consecutive changes
%p A374176 b:= n-> `if`(n<2, [0$2], (f-> (t-> [t, max(t, f[2])])(
%p A374176         `if`(n mod 4 in {0, 3}, 0, f[1]+1)))(b(iquo(n, 2)))):
%p A374176 a:= n-> b(n)[2]:
%p A374176 seq(a(n), n=1..105);  # _Alois P. Heinz_, Jul 07 2024
%o A374176 (PARI) a(n) = {my(b=digits(n,2), d=#b, m=0, j=b[1], c=0); for(k=2, d, if(b[k]!=j, c++; m=max(m,c), c=0); j=b[k]); m}
%o A374176 (Python)
%o A374176 def a(n):
%o A374176     b, c, m = bin(n)[2:], 0, 0
%o A374176     for i in range(len(b)-1):
%o A374176         if b[i] != b[i+1]: c += 1
%o A374176         else: m = max(m, c); c = 0
%o A374176     return max(m, c)
%o A374176 print([a(n) for n in range(1, 89)]) # _Michael S. Branicky_, Jul 06 2024
%o A374176 (Python) # using formula
%o A374176 from itertools import groupby
%o A374176 def a(n): return max((len(list(g)) for k, g in groupby(bin(n^(n>>1))[3:]) if k=="1"), default=0)
%o A374176 print([a(n) for n in range(1, 89)]) # _Michael S. Branicky_, Jul 06 2024
%Y A374176 Cf. A005811, A037834, A038554, A038374.
%Y A374176 Cf. A000975 (index of first occurrence of n).
%K A374176 nonn,base
%O A374176 1,5
%A A374176 _Hugo Pfoertner_, Jul 05 2024