A107483 Base 3 representation of the positive integers n such that Sum[d[k],k=1..n] is an integer, where d(k) is the base 3 fraction 0.k (e.g., d(22 base 10)=d(211 base 3)=0.221 base 3).

2, 20, 100, 122, 2222, 20000, 100000, 122222, 2222222, 20000000, 100000000, 122222222, 2222222222, 20000000000, 100000000000, 122222222222, 2222222222222, 20000000000000, 100000000000000, 122222222222222

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Formula

It appears that a(n)=2*(3^(3*k-1))-1 if n=4k, a(n)=3^(3*k+1)-1 if n=4k+1, a(n)=2*(3^(3*k+1)) if n=4k+2 and a(n)=3^(3*k+2) if n=4k+3.

From the above would follow that sequence has a rational g.f.

Empirical g.f.: 2*x*(50*x^6-100*x^5+90*x^4+20*x^3+41*x^2+9*x+1) / ((x-1)*(x^2+1)*(1000*x^4-1)). - Colin Barker, Nov 06 2014

Example

Sum[d(k), k=1..6](base 3) = (0.1+0.2+0.10+0.11+0.12+0.20)(base 3)=10.0 (base 3)=3 (base 10), hence 6 is in the sequence.

Crossrefs

Cf. A054464.

Sequence in context: A328510 A033840 A086755 * A356344 A220856 A035599

Adjacent sequences: A107480 A107481 A107482 * A107484 A107485 A107486

Keyword

nonn,base

Author

John W. Layman, Jun 09 2005

Status

approved