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Partial sums of A080278.
4

%I #32 May 01 2021 02:14:40

%S 1,2,6,7,8,12,13,14,27,28,29,33,34,35,39,40,41,54,55,56,60,61,62,66,

%T 67,68,108,109,110,114,115,116,120,121,122,135,136,137,141,142,143,

%U 147,148,149,162,163,164,168,169,170,174,175,176,216,217,218,222,223,224,228,229

%N Partial sums of A080278.

%H Klaus Brockhaus, <a href="/A080278/a080278.gif">Illustration of A080278 and A080333</a>

%H B. Dearden, J. Iiams, and J. Metzger, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Dearden/dearden3r.html">A Function Related to the Rumor Sequence Conjecture </a>, J. Int. Seq. 14 (2011) # 11.2.3.

%F a(n) = Sum_{k=0..log_3(n)} 3^k*floor(n/3^k).

%F a(3^k) = (k+1)*3^k.

%F a(n) is conjectured to be asymptotic to n*log(n)/log(3). - _Klaus Brockhaus_, Mar 23 2003 [This follows from the asymptotics of A333979. - _Pontus von Brömssen_, Sep 06 2020]

%F a(n) = n + 3*a(floor(n/3)), a(0)=0. - _Vladeta Jovovic_, Aug 06 2003

%F G.f.: (1/(1 - x))*Sum_{k>=0} 3^k*x^(3^k)/(1 - x^(3^k)). - _Ilya Gutkovskiy_, Mar 15 2018

%F a(n) = A333979(3*n,3). - _Pontus von Brömssen_, Sep 06 2020

%o (PARI) a(n) = fromdigits(Vec(Pol(digits(3*n,3))'),3); \\ _Kevin Ryde_, Apr 29 2021

%Y Cf. A080277, A080278, A333979.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 19 2003