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 A051064 3^a(n) exactly divides 3n. Or, 3-adic valuation of 3n. 23
 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 5, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is the Hamming distance between n and n-1 in ternary representation. - Philippe Deléham, Mar 29 2004 Also : 3^a(n) divides exactly 4^n-1. - Benoit Cloitre, Oct 25 2004 Generalized Ruler Function for k=3 - Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca) a(A007417(n)) is odd and a(A145204(n)) is even. - Reinhard Zumkeller, May 23 2013 First n terms comprise least cubefree word of length n using positive integers, where "cubefree" means that the word contains no three consecutive identical subwords; e.g., 1 contains no cube; 11 contains no cube; 111 does but 112 does not; ... 1,1,2,1,1,2,1,1,1 does, and 1,1,2,1,1,2,1,1,2 does, but 1,1,2,1,1,2,1,1,3 does not, etc. - Clark Kimberling, Sep 10 2013 The sequence is invariant under the "lower trim" operator: remove all ones, and subtract one from each remaining term. - Franklin T. Adams-Watters, May 25 2017 REFERENCES Letter from Gary W. Adamson to N. J. A. Sloane concerning Prouhet-Thue-Morse sequence, Nov. 11, 1999. LINKS T. D. Noe, Table of n, a(n) for n=1..1000 A. M. Hinz, S. Klavžar, U. Milutinović, C. Petr, The Tower of Hanoi - Myths and Maths, Birkhäuser 2013. See page 243. Book's website Simon Plouffe, On the values of the functions ... [zeta and Gamma] ..., arXiv preprint arXiv:1310.7195, 2013 FORMULA Multiplicative with a(p^e) = e+1 if p = 3; 1 if p <> 3. - Vladeta Jovovic, Aug 24 2002 G.f.: Sum(k>=0, x^3^k/(1-x^3^k)). - Ralf Stephan, Apr 12 2002 Fixed point of the morphism: 1 -> 112; 2 -> 113; 3 -> 114; 4 -> 115; ...; starting from a(1) = 1. a(3n+1) = a(3n+2) = 1; a(3n) = 1 + a(n). - Philippe Deléham, Mar 29 2004 a(n) = (-1)*sum_{d divides n} mu(3d)*tau(n/d). - Benoit Cloitre, Jun 21 2007 Dirichlet g.f. zeta(s)/(1-1/3^s). - R. J. Mathar, Jun 13 2011 a(n) = 1/2*(3 - A053735(n) + A053735(n-1)) for n >= 1. - Tom Edgar, Aug 06 2014 a(n) = A007949(3n). - Cyril Damamme, Aug 04 2015 a(2n) = a(n), a(2n-1) = A254046(n). - Cyril Damamme, Aug 04 2015 EXAMPLE 3^2 | 3*6 = 18, so a(6) = 2. MAPLE seq(1+padic:-ordp(n, 3), n=1..100); # Robert Israel, Aug 07 2014 MATHEMATICA Nest[ Function[ l, {Flatten[(l /. {1 -> {1, 1, 2}, 2 -> {1, 1, 3}, 3 -> {1, 1, 4}, 4 -> {1, 1, 5}})]}], {1}, 5] (* Robert G. Wilson v, Mar 03 2005 *) Table[ IntegerExponent[3n, 3], {n, 1, 105}] (* Jean-François Alcover, Oct 10 2011 *) PROG (PARI) a(n)=if(n<1, 0, 1+valuation(n, 3)) (Haskell) a051064 = (+ 1) . length .                   takeWhile (== 3) . dropWhile (== 2) . a027746_row -- Reinhard Zumkeller, May 23 2013 CROSSREFS a(n) = A007949(n)+1 = A004128(n)-A004128(n-1). Cf. A001511, A007949. Partial sums give A004128. Cf. A027746. Cf. A254046. Sequence in context: A101022 A241153 A213852 * A280509 A153096 A210763 Adjacent sequences:  A051061 A051062 A051063 * A051065 A051066 A051067 KEYWORD nonn,easy,nice,mult,changed AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 11 1999 More terms from Vladeta Jovovic, Aug 24 2002 STATUS approved

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