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A053838 a(n) = (sum of digits of n written in base 3) modulo 3. 18
0, 1, 2, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 1, 0, 1, 2, 1, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Start with 0, repeatedly apply the morphism 0->012, 1->120, 2->201. This is a ternary version of the Thue-Morse sequence A010060. See Brlek (1989). - N. J. A. Sloane, Jul 10 2012
Equals A004128 mod 3. [Gary W. Adamson, Aug 24 2008]
A090193 is generated by the same mapping starting with 1. A090239 is generated by the same mapping starting with 2. - Andrey Zabolotskiy, May 04 2016.
LINKS
S. Brlek, Enumeration of factors in the Thue-Morse word, Discrete Applied Math. 24 (1989), 83-96.
Arthur Dolgopolov, Equitable Sequencing and Allocation Under Uncertainty, Preprint, 2016.
Glen Joyce C. Dulatre, Jamilah V. Alarcon, Vhenedict M. Florida, Daisy Ann A. Disu, On Fractal Sequences, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 109-113.
Michel Rigo, Relations on words, arXiv preprint arXiv:1602.03364 [cs.FL], 2016. See Example 17.
FORMULA
a(n) = A010872(A053735(n)) =(n+a(floor[n/3])) mod 3. So one can construct sequence by starting with 0 and mapping 0->012, 1->120 and 2->201 (e.g. 0, 012, 012120201, 012120201120201012201012120, ...) and looking at n-th digit of a term with sufficient digits.
MAPLE
A053838 := proc(n)
add(d, d=convert(n, base, 3)) ;
modp(%, 3) ;
end proc:
seq(A053838(n), n=0..100) ; # R. J. Mathar, Nov 04 2017
MATHEMATICA
Nest[ Flatten[ # /. {0 -> {0, 1, 2}, 1 -> {1, 2, 0}, 2 -> {2, 0, 1}}] &, {0}, 7] (* Robert G. Wilson v, Mar 08 2005 *)
PROG
(PARI) a(n) = vecsum(digits(n, 3)) % 3; \\ Michel Marcus, May 04 2016
CROSSREFS
Equals A026600(n+1) - 1.
Sequence in context: A258196 A159955 A327306 * A342651 A275768 A117167
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)