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A106701
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a(n) = next-to-most-significant binary digit of n-th composite positive integer.
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2
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0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 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, 1, 1, 0, 0, 0, 0, 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, 1, 1, 1, 1, 0, 0, 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 each run of zeros and ones: 1,3,6,13,25,53,107,219,445,899,1821,... and 1,3,5,12,26,52,106,218,442,894,1811,2838,..., . - Robert G. Wilson v.
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FORMULA
| a(n) = floor((c(n) - 2^m)/2^(m-1)), where c(n) is the n-th composite and m = floor(ln(c(n))/ln(2)).
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EXAMPLE
| a(2) = 1 because 6 is the second composite and because the next-to-most-significant binary digit (which happens to be the middle binary digit) of 6 = 110 (in binary) is 1.
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MATHEMATICA
| f[n_] := IntegerDigits[ FixedPoint[n + PrimePi[ # ] + 1 &, n], 2][[2]]; Array[f, 105] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A115454, A112416.
Sequence in context: A076478 A091444 A091447 * A033684 A080885 A068716
Adjacent sequences: A106698 A106699 A106700 * A106702 A106703 A106704
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KEYWORD
| base,nonn
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AUTHOR
| Leroy Quet, Jan 22 2006
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 24 2006
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