%I A006345 M0074
%S A006345 1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1,2,1,1,1,2,2,1,2,1,1,2,2,1,1,1,2,1,1,2,
%T A006345 2,1,2,1,1,2,1,2,2,1,1,2,1,1,1,2,2,1,2,1,1,2,2,1,2,2,2,1,1,2,1,2,2,1,1,
%U A006345 2,2,2,1,2,2,1,1,2,1,2,2,1,2,1,1,2,2,1,2,2,2,1,1,2,1,2,2,1,1,2,2,2,1,2
%N A006345 Linus sequence: a(n) "breaks the pattern" by avoiding the longest doubled 
               suffix.
%C A006345 To compute a(n), consider either a 1 or a 2. For each, find the longest 
               repeated suffix, that is, for each of a(n)=1,2, find the longest 
               sequence s with the property that the sequence a(1),...,a(n) ends 
               with ss. Use the digit that results in the shorter such suffix. a(1) 
               = 1. The empty sequence of length 0 is the shortest possible suffix 
               and is trivially doubled. Note that this doesn't result in exactly 
               Linus's choices (K. Ramsey, kramsey(AT)aol.com).
%D A006345 N. S. Hellerstein, personal communication.
%D A006345 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006345 T. D. Noe, <a href="b006345.txt">Table of n, a(n) for n=1..1000</a>
%H A006345 N. J. A. Sloane, <a href="a6345.html">Illustration of initial terms</
               a>
%H A006345 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LinusSequence.html">Link to a section of The World of Mathematics.</
               a>
%e A006345 After 1,2,1,1,2,2,1,2, if we put a 1, the suffix {2,1} repeats, but if 
               we put a 2 the longer suffix {1,2,2} repeats, so the next term is 
               1.
%o A006345 (Perl) -le 'print$_.=3**/(.*)(.)\1$/-$2for($_)x99' (Ton Hospel/Phil Carmody) 
               [An example of Perl golfing: use as few (key)strokes as possible]
%o A006345 (PARI) {a(n)=local(A,t); if(n<2, n>0, A=[1]; for(i=2, n, forstep(j=i\2-1, 
               0, -1, for(k=1, j, if(A[i-j-k-1]!=A[i-k], next(2))); t=j; break); 
               A=concat(A,[3-A[i-t-1]])); A[n])} /* Michael Somos May 04 2006 */
%Y A006345 Cf. A006346.
%Y A006345 Sequence in context: A051287 A049705 A060236 this_sequence A122497 A154402 
               A023396
%Y A006345 Adjacent sequences: A006342 A006343 A006344 this_sequence A006346 A006347 
               A006348
%K A006345 nonn,easy,nice
%O A006345 1,2
%A A006345 N. J. A. Sloane (njas(AT)research.att.com).
%E A006345 More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), May 21 
               2001
%E A006345 Additional comments from Mitch Harris, Dec 31, 2003