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A006345
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Linus sequence: a(n) "breaks the pattern" by avoiding the longest doubled suffix.
(Formerly M0074)
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3
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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).
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REFERENCES
| N. S. Hellerstein, personal communication to N. J. A. Sloane.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
N. J. A. Sloane, Illustration of initial terms
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
| 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.
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PROG
| (Perl) -le 'print$_.=3**/(.*)(.)\1$/-$2for($_)x99' (Ton Hospel/Phil Carmody) [An example of Perl golfing: use as few (key)strokes as possible]
(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 */
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CROSSREFS
| Cf. A006346.
Sequence in context: A202340 A049705 A060236 * A122497 A154402 A177025
Adjacent sequences: A006342 A006343 A006344 * A006346 A006347 A006348
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), May 21 2001
Additional comments from Mitch Harris, Dec 31, 2003
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