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A092339
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Number of adjacent identical digits in the binary representation of n.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| In binary: number of 00 blocks plus number of 11 blocks.
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REFERENCES
| J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 84.
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FORMULA
| Recurrence: a(2n) = a(n) + [n even], a(2n+1) = a(n) + [n odd].
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EXAMPLE
| 60 in binary is 111100, it has 4 blocks of adjacent digits, so a(60)=4.
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PROG
| (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
| A014081(n) + A056973(n). Cf. A005811.
Sequence in context: A108423 A193804 A180424 * A079693 A117444 A015504
Adjacent sequences: A092336 A092337 A092338 * A092340 A092341 A092342
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 18 2004
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