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Search: id:A060236
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| A060236 |
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If n mod 3 = 0 then a(n)=a(n/3), otherwise a(n)=n mod 3. |
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+0
6
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| 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A cube-free word. Start with 1, apply the morphisms 1 -> 121, 2 -> 122, take limit. See A080846 for another version.
Ultimate modulo 3: n-th digit of terms in "Ana sequence" (see A060032 for definition).
Equals A005148(n) reduced mod 3. In "On a sequence Arising in Series for Pi" Morris Newman and Daniel Shanks conjectured that 3 never divides A005148(n) and D. Zagier proved it. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 22 2002
Also equals A038502(n) mod 3.
Last nonzero digit in ternary representation of n. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 01 2006
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REFERENCES
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J. Berstel and J. Karhumaki, Combinatorics on words - a tutorial, Bull. EATCS, #79 (2003), pp. 178-228.
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LINKS
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Jean Berstel, Home Page
Index entries for sequences related to final digits of numbers
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FORMULA
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a(3*n) = a(n), a(3*n + 1) = 1, a(3*n + 2) = 2. - Michael Somos Jul 29 2009
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EXAMPLE
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a(10)=1 since 10=3^0*10 and 10 mod 3=1; a(72)=2 since 24=3^3*8 and 8 mod 3=2.
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MATHEMATICA
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Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, 5] (from Robert G. Wilson v Mar 04 2005)
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PROGRAM
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(PARI) a(n)=if(n<1, 0, n/3^valuation(n, 3)%3) /* Michael Somos Nov 10 2005 */
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CROSSREFS
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Cf. A026140 and A026225 for sequence of n's for which a(n)=1, A026179 for sequence of n's for which a(n)=2. k-th term of A060032 is concatenation of first 3^k terms of a(n).
Sequence in context: A156074 A051287 A049705 this_sequence A006345 A122497 A154402
Adjacent sequences: A060233 A060234 A060235 this_sequence A060237 A060238 A060239
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 21 2001
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