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A113217
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Parity of decimal digital root of n.
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4
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0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1
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OFFSET
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0,1
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COMMENTS
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Except for the first element, the sequence is periodic (with a period of length 9). The sequence corresponds to that produced by a prescribed set of bitwise operations. The (sub)sequence is produced starting from input pairs (0,1),(1,1),(1,0). For example, (0,1) acted on (in succession) by [and,xor,or,xor,or,and,or,and,xor], with the same operation set then repeated. For clarity, the example is AND(0,1) is 0. XOR(1,0) is 1. OR(0,1) is 1. XOR(1,1) is 0. OR(1,0) is 1. AND(0,1) is 0. OR(1,0) is 1. AND(0,1) is 0. XOR(1,0) is 1. Repeat. The analysis was done using Gnumeric's built-in functions. In this example, the inputs align to n=2,3, and the operation results to the next 7 elements. The (3) starting input pairs mentioned begin at bitwise operator positions 1,2 and 5. - Bill McEachen, May 24 2014
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LINKS
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Table of n, a(n) for n=0..104.
MathWorld, Digital Root
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FORMULA
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a(n) = A010888(n) mod 2.
a(n) = if n mod 9 = 1 then 1 else 1 - a(n-1), a(0)=0.
a(n) = A000035(A010888(n)). - Omar E. Pol, Oct 28 2013
a(n) = (1+(-1)^floor(8*n/9))/2 for n>0. - Wesley Ivan Hurt, Apr 27 2020
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CROSSREFS
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Cf. A113218.
Sequence in context: A073445 A285589 A179081 * A189219 A189008 A285515
Adjacent sequences: A113214 A113215 A113216 * A113218 A113219 A113220
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KEYWORD
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nonn,base,easy
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AUTHOR
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Reinhard Zumkeller, Oct 18 2005
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STATUS
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approved
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