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A112416
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Next-to-most-significant binary digit of the n-th prime.
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2
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0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The length of the run of zeros pi(2^n+2^(n-1))-pi(2^n) (A095765): 1, 1, 1, 3, 4, 6, 12, 22, 38, 70, 130, 237, 441, ... and the length of the run of ones pi(2^n-1)-pi(2^n-2^(n-2)-1) (A095766): 1, 1, 1, 2, 3, 7, 11, 21, 37, 67, 125, 227, 431, ..., . (Robert G. Wilson v)
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FORMULA
| a(n) = floor((p(n) - 2^m)/2^(m-1)), where p(n) is the n-th prime and m = floor(ln(p(n))/ln(2)).
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EXAMPLE
| The 9th prime is 23 (in decimal), which is 10111 in binary. So a(9) = 0, the next-to-most significant binary digit of 23.
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MATHEMATICA
| f[n_] := IntegerDigits[Prime@n, 2][[2]]; Array[f, 105] (Robert G. Wilson v)
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CROSSREFS
| Cf. A004676, A106701.
Sequence in context: A082848 A173922 A141743 * A061265 A139312 A173923
Adjacent sequences: A112413 A112414 A112415 * A112417 A112418 A112419
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KEYWORD
| base,nonn
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AUTHOR
| Leroy Quet, Dec 09 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 24 2006
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