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 A164349 #22 Aug 02 2015 02:07:45 %S A164349 0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0, %T A164349 1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0, %U A164349 0,1,0,1,0,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0,0,1,0,1 %N A164349 The limit of the string "0, 1" under the operation 'repeat string twice and remove last symbol'. %C A164349 We start with the string 01, at each step we replace the string by two concatenated copies and remove the last symbol. %C A164349 01 -> 010 -> 01001 -> 010010100 etc. %C A164349 Each string consists of 2^n + 1 symbols and clearly after this step the first 2^n + 1 symbols do not change. %C A164349 Equivalently this sequence is given as follows: a(0) = 0, a(1) = 1, and for n>1, a(n) = first one of g(n), g(g(n)), g(g(g(n))).. etc. to be either 0 or 1, where g(n) = A053645(n-1). %C A164349 The proportion of 0's in this sequence converges to a number close to 0.645059. The exact nature of this constant is not known. It is easy to show there are no 2 consecutive 1's. %C A164349 Start of the first occurrence of k consecutive zeros: 0, 2, 7, 2046, > 8388600, ..., . - _Robert G. Wilson v_, Aug 17 2009 %C A164349 Start of the first occurrence of 5 consecutive zeros is > 2^34 - 5. Sum of the first 10^n terms b(n) begins: 0, 3, 36, 355, 3549, 35494, 354942, 3549412, 35494122, 354941215, 3549412151. - _Alex Ratushnyak_, Aug 15 2012 %C A164349 a(A246439(n)) = 1; a(A246438(n)) = 0. - _Reinhard Zumkeller_, Aug 28 2014 %C A164349 The partial sums appear to give A101402. - _Arie Groeneveld_, Aug 27 2014 %H A164349 Robert G. Wilson v, <a href="/A164349/b164349.txt">Table of n, a(n) for n = 0..16384 </a> %t A164349 Nest[ Most@ Flatten@ {#, #} &, {0, 1}, 7] (* _Robert G. Wilson v_, Aug 17 2009 *) %o A164349 (Perl) my $ab = "10"; for (my $j = 1; $j < 30; $j++) { $ab .= $ab; substr $ab, -1, 1, ""; print "$ab\n"; } %o A164349 (Haskell) %o A164349 a164349 n = if n == 0 then 0 else until (<= 1) (a053645 . subtract 1) n %o A164349 -- _Reinhard Zumkeller_, Aug 28 2014 %Y A164349 Cf. A053645, A246438, A246439, A101402. %K A164349 easy,nonn %O A164349 0,1 %A A164349 _Jack W Grahl_, Aug 13 2009 %E A164349 Spelling and notation corrected by _Charles R Greathouse IV_, Mar 23 2010