A080333 Partial sums of A080278.

1, 2, 6, 7, 8, 12, 13, 14, 27, 28, 29, 33, 34, 35, 39, 40, 41, 54, 55, 56, 60, 61, 62, 66, 67, 68, 108, 109, 110, 114, 115, 116, 120, 121, 122, 135, 136, 137, 141, 142, 143, 147, 148, 149, 162, 163, 164, 168, 169, 170, 174, 175, 176, 216, 217, 218, 222, 223, 224, 228, 229

Offset: 1

Author

N. J. A. Sloane, Mar 19 2003

Keywords

• nonn

Links

• Klaus Brockhaus, Illustration of A080278 and A080333
• B. Dearden, J. Iiams, and J. Metzger, A Function Related to the Rumor Sequence Conjecture , J. Int. Seq. 14 (2011) # 11.2.3.

Crossrefs

Cf. A080277, A080278, A333979.

Programs

PARI

a(n) = fromdigits(Vec(Pol(digits(3*n,3))'),3); \\ Kevin Ryde, Apr 29 2021

Formula

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

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

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]

a(n) = n + 3*a(floor(n/3)), a(0)=0. - Vladeta Jovovic, Aug 06 2003

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

a(n) = A333979(3*n,3). - Pontus von Brömssen, Sep 06 2020