A092339 - OEIS

%I #17 Mar 11 2015 15:19:59

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

%T 2,3,2,1,2,3,2,1,0,1,2,1,2,3,4,3,2,3,2,1,2,3,4,3,2,3,4,3,4,5,5,4,3,4,

%U 3,2,3,4,3,2,1,2,3,2,3,4,3,2,1,2,1,0,1,2,3,2,1,2,3,2,3,4,5,4,3,4,3,2

%N Number of adjacent identical digits in the binary representation of n.

%C In binary: number of 00 blocks plus number of 11 blocks. (Note: the blocks can overlap. See the example below.)

%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 84.

%F Recurrence: a(2n) = a(n) + [n even], a(2n+1) = a(n) + [n odd].

%F a(n) = A014081(n) + A056973(n).

%F For n>0, A227185(n) = a(n)+1.

%F a(n) = A080791(A003188(n)) [because the sequence gives the number of nonleading zeros in binary Gray code expansion of n] - _Antti Karttunen_, Jul 05 2013

%e 60 in binary is 111100, it has 4 blocks of adjacent digits, so a(60)=4.

%e Equally, 60's binary Gray code expansion is A003188(60)=34, 100010 in binary, which contains four zeros.

%o (PARI) a(n)=local(v); v=binary(n); sum(k=1, length(v)-1, v[k]==v[k+1])

%o (PARI) a(n)=if(n<1,0,if(n%2==0,a(n/2)+(n>0&&(n/2)%2==0),a((n-1)/2)+((n-1)/2)%2))

%o (Scheme) (define (A092339 n) (A080791 (A003188 n))) ;; _Antti Karttunen_, Jul 05 2013

%Y Cf. A005811.

%K nonn,base

%O 0,8

%A _Ralf Stephan_, Mar 18 2004