Search: id:A007949
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%I A007949
%S A007949 0,0,1,0,0,1,0,0,2,0,0,1,0,0,1,0,0,2,0,0,1,0,0,1,0,0,3,0,0,1,0,0,1,0,0,
%T A007949 2,0,0,1,0,0,1,0,0,2,0,0,1,0,0,1,0,0,3,0,0,1,0,0,1,0,0,2,0,0,1,0,0,1,0,
%U A007949 0,2,0,0,1,0,0,1,0,0,4,0,0,1,0,0,1,0,0,2,0,0,1,0,0,1,0,0,2,0,0,1,0,0,1
%N A007949 Greatest k such that 3^k divides n. Or, 3-adic valuation of n.
%C A007949 a(n) mod 2 = 1 - A014578(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 04 2008]
%D A007949 K. Atanassov, On the 61-st, 62-nd and the 63-rd Smarandache Problems, 
               Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, 
               Vol. 4 (1998), No. 4, 175-182.
%D A007949 K. Atanassov, On Some of Smarandache's Problems, American Research Press, 
               1999, 16-21.
%D A007949 F. Q. Gouvea, p-Adic Numbers, Springer-Verlag, 1993; see p. 23.
%D A007949 F. Smarandache, Only Problems, not Solutions!, Xiquan Publ., Phoenix-Chicago, 
               1993.
%D A007949 M. Vassilev-Missana and K. Atanassov, Some Representations related to 
               n!, Notes on Number Theory and Discrete Mathematics, Vol. 4 (1998), 
               No. 4, 148-153.
%H A007949 T. D. Noe, <a href="b007949.txt">Table of n, a(n) for n=1..1000</a>
%H A007949 K. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">
               On Some of Smarandache's Problems</a>
%H A007949 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A007949 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>.
%F A007949 a(n) = if n > 0 modulo 3 then 0 else 1 + a(n/3). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Aug 12 2001
%F A007949 a(n)=A051064(n)-1. G.f.: Sum(k>=1, x^3^k/(1-x^3^k)))). - Ralf Stephan 
               (ralf(AT)ark.in-berlin.de), Apr 12 2002
%F A007949 Fixed point of the morphism : 0 -> 001; 1 -> 002; 2 -> 003; 3 -> 004; 
               4 -> 005; etc...; starting from a(1) = 0. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Mar 29 2004
%F A007949 Totally additive with a(p) = 1 if p = 3, 0 otherwise.
%p A007949 A007949 := proc(n) option remember; if n mod 3 > 0 then 0 else A007949(n/
               3)+1; fi; end;
%t A007949 p=3; Array[ If[ Mod[ #, p ]==0, Select[ FactorInteger[ # ], Function[ 
               q, q[ [ 1 ] ]==p ], 1 ][ [ 1, 2 ] ], 0 ]&, 81 ]
%t A007949 Nest[ Function[ l, {Flatten[(l /. {0 -> {0, 0, 1}, 1 -> {0, 0, 2}, 2 
               -> {0, 0, 3}, 3 -> {0, 0, 4}}) ]}], {0}, 5] (from Robert G. Wilson 
               v Mar 03 2005)
%o A007949 (PARI) a(n)=valuation(n,3)
%Y A007949 Partial sums give A054861. Cf. A080278, A001511.
%Y A007949 Cf. A122841, A007814, A112765.
%Y A007949 Sequence in context: A016380 A015692 A016232 this_sequence A078595 A078128 
               A112607
%Y A007949 Adjacent sequences: A007946 A007947 A007948 this_sequence A007950 A007951 
               A007952
%K A007949 nonn,easy
%O A007949 1,9
%A A007949 R. Muller

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