This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080333 #32 May 01 2021 02:14:40
%S A080333 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 A080333 67,68,108,109,110,114,115,116,120,121,122,135,136,137,141,142,143,
%U A080333 147,148,149,162,163,164,168,169,170,174,175,176,216,217,218,222,223,224,228,229
%N A080333 Partial sums of A080278.
%H A080333 Klaus Brockhaus, <a href="/A080278/a080278.gif">Illustration of A080278 and A080333</a>
%H A080333 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 A080333 a(n) = Sum_{k=0..log_3(n)} 3^k*floor(n/3^k).
%F A080333 a(3^k) = (k+1)*3^k.
%F A080333 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 A080333 a(n) = n + 3*a(floor(n/3)), a(0)=0. - _Vladeta Jovovic_, Aug 06 2003
%F A080333 G.f.: (1/(1 - x))*Sum_{k>=0} 3^k*x^(3^k)/(1 - x^(3^k)). - _Ilya Gutkovskiy_, Mar 15 2018
%F A080333 a(n) = A333979(3*n,3). - _Pontus von Brömssen_, Sep 06 2020
%o A080333 (PARI) a(n) = fromdigits(Vec(Pol(digits(3*n,3))'),3); \\ _Kevin Ryde_, Apr 29 2021
%Y A080333 Cf. A080277, A080278, A333979.
%K A080333 nonn
%O A080333 1,2
%A A080333 _N. J. A. Sloane_, Mar 19 2003