Search: id:A060236
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%I A060236
%S A060236 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,
%T A060236 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,
%U A060236 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
%N A060236 If n mod 3 = 0 then a(n)=a(n/3), otherwise a(n)=n mod 3.
%C A060236 A cube-free word. Start with 1, apply the morphisms 1 -> 121, 2 -> 122, 
               take limit. See A080846 for another version.
%C A060236 Ultimate modulo 3: n-th digit of terms in "Ana sequence" (see A060032 
               for definition).
%C A060236 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
%C A060236 Also equals A038502(n) mod 3.
%C A060236 Last nonzero digit in ternary representation of n. - Frank Adams-Watters 
               (FrankTAW(AT)Netscape.net), Apr 01 2006
%D A060236 J. Berstel and J. Karhumaki, Combinatorics on words - a tutorial, Bull. 
               EATCS, #79 (2003), pp. 178-228.
%H A060236 Jean Berstel, <a href="http://www-igm.univ-mlv.fr/~berstel/">Home Page</
               a>
%H A060236 <a href="Sindx_Fi.html#final">Index entries for sequences related to 
               final digits of numbers</a>
%F A060236 a(3*n) = a(n), a(3*n + 1) = 1, a(3*n + 2) = 2. - Michael Somos Jul 29 
               2009
%e A060236 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.
%t A060236 Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, 5] (from 
               Robert G. Wilson v Mar 04 2005)
%o A060236 (PARI) a(n)=if(n<1, 0, n/3^valuation(n,3)%3) /* Michael Somos Nov 10 
               2005 */
%Y A060236 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).
%Y A060236 Sequence in context: A156074 A051287 A049705 this_sequence A006345 A122497 
               A154402
%Y A060236 Adjacent sequences: A060233 A060234 A060235 this_sequence A060237 A060238 
               A060239
%K A060236 easy,nonn
%O A060236 1,2
%A A060236 Henry Bottomley (se16(AT)btinternet.com), Mar 21 2001

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