Search: id:A106701
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%I A106701
%S A106701 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,
%T A106701 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,
%U A106701 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
%N A106701 a(n) = next-to-most-significant binary digit of n-th composite positive 
               integer.
%C A106701 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.
%H A106701 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A106701 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)).
%e A106701 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.
%t A106701 f[n_] := IntegerDigits[ FixedPoint[n + PrimePi[ # ] + 1 &, n], 2][[2]]; 
               Array[f, 105] (* Robert G. Wilson v *)
%Y A106701 Cf. A115454, A112416.
%Y A106701 Sequence in context: A076478 A091444 A091447 this_sequence A033684 A080885 
               A068716
%Y A106701 Adjacent sequences: A106698 A106699 A106700 this_sequence A106702 A106703 
               A106704
%K A106701 base,nonn
%O A106701 1,1
%A A106701 Leroy Quet, Jan 22 2006
%E A106701 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 24 2006

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