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A113217 Parity of decimal digital root of n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
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
LINKS
MathWorld, Digital Root
FORMULA
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
CROSSREFS
Cf. A113218.
Sequence in context: A073445 A285589 A179081 * A189219 A189008 A353681
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Zumkeller, Oct 18 2005
STATUS
approved

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Last modified March 19 06:29 EDT 2024. Contains 370953 sequences. (Running on oeis4.)