Search: id:A112416
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%I A112416
%S A112416 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,
%T A112416 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,
%U A112416 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
%N A112416 Next-to-most-significant binary digit of the n-th prime.
%C A112416 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)
%H A112416 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A112416 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)).
%e A112416 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.
%t A112416 f[n_] := IntegerDigits[Prime@n, 2][[2]]; Array[f, 105] (Robert G. Wilson 
               v)
%Y A112416 Cf. A004676, A106701.
%Y A112416 Sequence in context: A154104 A082848 A141743 this_sequence A061265 A125122 
               A000035
%Y A112416 Adjacent sequences: A112413 A112414 A112415 this_sequence A112417 A112418 
               A112419
%K A112416 base,nonn
%O A112416 1,1
%A A112416 Leroy Quet, Dec 09 2005
%E A112416 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 24 2006

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