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

1,2

Links

Table of n, a(n) for n=1..61.

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.

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

Prog

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

Crossrefs

Cf. A080277, A080278, A333979.

Sequence in context: A275523 A327258 A047240 * A194369 A039592 A037454

Adjacent sequences: A080330 A080331 A080332 * A080334 A080335 A080336

Keyword

nonn

Author

N. J. A. Sloane, Mar 19 2003

Status

approved