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 A060236 If n mod 3 = 0 then a(n) = a(n/3), otherwise a(n) = n mod 3. 7
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A cubefree 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, Jun 22 2002 Also equals A038502(n) mod 3. Last nonzero digit in ternary representation of n. - Franklin T. Adams-Watters, Apr 01 2006 a(2*n) = length of n-th run of twos. - Reinhard Zumkeller, Mar 13 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Jean Berstel and J. Karhumaki, Combinatorics on words - a tutorial, Bull. EATCS, #79 (2003), pp. 178-228. FORMULA a(3*n) = a(n), a(3*n + 1) = 1, a(3*n + 2) = 2. - Michael Somos, Jul 29 2009 a(n) = 1 + A080846(n). - Joerg Arndt, Jan 21 2013 nts of mappings EXAMPLE 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. MATHEMATICA Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, 5] (* Robert G. Wilson v, Mar 04 2005 *) lnzd[m_]:=Module[{s=Split[m]}, If[FreeQ[Last[s], 0], s[[-1, 1]], s[[-2, 1]]]]; lnzd/@Table[IntegerDigits[n, 3], {n, 120}] (* Harvey P. Dale, Oct 19 2018 *) PROG (PARI) a(n)=if(n<1, 0, n/3^valuation(n, 3)%3) /* Michael Somos, Nov 10 2005 */ (Haskell)  following Franklin T. Adams-Watters' comment. a060236 = head . dropWhile (== 0) . a030341_row -- Reinhard Zumkeller, Mar 13 2015 Table[Mod[n/3^IntegerExponent[n, 3], 3], {n, 1, 120}] (* Clark Kimberling, Oct 19 2016 *) CROSSREFS 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). Cf. A030341, A007089. Sequence in context: A265209 A202340 A049705 * A006345 A122497 A154402 Adjacent sequences:  A060233 A060234 A060235 * A060237 A060238 A060239 KEYWORD easy,nonn AUTHOR Henry Bottomley, Mar 21 2001 STATUS approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)