This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A106701 #15 Mar 20 2015 23:18:04 %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, %T A106701 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, %U A106701 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 %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_ %F A106701 a(n) = floor((c(n) - 2^m)/2^(m-1)), where c(n) is the n-th composite and m = floor(log(c(n))/log(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. %K A106701 base,nonn %O A106701 1,1 %A A106701 _Leroy Quet_, Jan 22 2006 %E A106701 More terms from _Robert G. Wilson v_, Jan 24 2006