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A092339
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Number of adjacent identical digits in the binary representation of n.
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7
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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, 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, 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
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OFFSET
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0,8
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COMMENTS
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In binary: number of 00 blocks plus number of 11 blocks. (Note: the blocks can overlap. See the example below.)
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 84.
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LINKS
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FORMULA
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Recurrence: a(2n) = a(n) + [n even], a(2n+1) = a(n) + [n odd].
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
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EXAMPLE
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60 in binary is 111100, it has 4 blocks of adjacent digits, so a(60)=4.
Equally, 60's binary Gray code expansion is A003188(60)=34, 100010 in binary, which contains four zeros.
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PROG
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(PARI) a(n)=local(v); v=binary(n); sum(k=1, length(v)-1, v[k]==v[k+1])
(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))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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