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A042974
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n 1's followed by a 2.
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8
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1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,2
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COMMENTS
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Fixed point of the following mapping w. Suppose x(n) takes values in {1,2} and w(n)=[x(1),x(2),...,x(n)]. Next define w(n+1)=[x(1),x(2),...,x(n),x(n-1)] if x(n)=1 and w(n+1)=[x(1),x(2),...,x(n),x(n-1),x(n-1)] if x(n)=2. Then taking x(1)=1 and x(2)=2 we get w(infinity)=A042974 (i.e., x(n)=A042974(n)). - Benoit Cloitre, Jan 11 2013
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LINKS
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EXAMPLE
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0.1211211121111211111211111121111111211111111211111111121111111111211111...
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MATHEMATICA
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Table[PadLeft[{2}, n, 1], {n, 2, 20}]//Flatten (* Harvey P. Dale, Sep 11 2019 *)
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PROG
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(PARI) {a(n) = 1 + issquare(9 + 8*n)}; /* Michael Somos, Jan 12 2000 */
(PARI) { default(realprecision, 20080); x=0; for (n=1, 20000, x=10*x + 1 + issquare(9+8*n)); x/=10^19999; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b042974.txt", n, " ", d)); } \\ Harry J. Smith, May 08 2009
(Haskell)
a042974 n = a042974_list !! (n-1)
a042974_list = 1 : 2 :
concat (zipWith replicate (tail a042974_list) a042974_list)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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