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A125047
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Infinite word generated by mapping 1->12, 2->13, 3->43, 4->42 starting at 1.
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2
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1, 2, 1, 3, 1, 2, 4, 3, 1, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 4, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 1, 2, 1, 3, 4, 2, 4, 3, 4, 2, 1, 3, 1, 2, 4, 3, 4, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 1, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 4, 2, 1, 3, 4, 2, 4, 3, 4, 2, 1, 3, 1, 2, 4, 3, 1
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OFFSET
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1,2
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COMMENTS
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Infinite word over 4-letter alphabet that contains no squares in arithmetic progressions of odd difference. - Ralf Stephan, May 09 2007
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LINKS
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Jui-Yi Kao, Narad Rampersad, Jeffrey Shallit, Manuel Silva, Words avoiding repetitions in arithmetic progressions, Theoretical Computer Science, volume 391, issues 1-2, February 2008, pages 126-137. And arXiv:math/0608607 [math.CO], 2006.
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FORMULA
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Recurrence: a(1)=1, a(4n)=3, a(4n+2)=2, a(8n+3)=1, a(8n+7)=4, a(4n+1)=a(2n+1). - Ralf Stephan, May 09 2007
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EXAMPLE
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1 -> 12 -> 1213 -> 12131242 -> 1213124312134243 -> ...
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MATHEMATICA
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SubstitutionSystem[{1 -> {1, 2}, 2 -> {1, 3}, 3 -> {4, 3}, 4 -> {4, 2}}, {1}, 7] // Last (* Jean-François Alcover, Dec 17 2018 *)
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PROG
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(PARI) {a(n)=local(A); if(n<1, 0, A=[1]; while(length(A)<n, A=concat(vector(length(A), k, [[1, 2], [1, 3], [4, 3], [4, 2]][A[k]]))); A[n])}
(PARI) my(table=[1, 2; 4, 3]); a(n) = n--; table[if(n, bittest(n, 1+valuation(n, 2)))+1, n%2+1]; \\ Kevin Ryde, Sep 05 2020
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CROSSREFS
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Essentially the same: A112658 (map 1234 -> 1023), A122002 (map 1234 -> 5137).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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