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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. 0
2, 20, 100, 122, 2222, 20000, 100000, 122222, 2222222, 20000000, 100000000, 122222222, 2222222222, 20000000000, 100000000000, 122222222222, 2222222222222, 20000000000000, 100000000000000, 122222222222222 (list; graph; refs; listen; history; text; internal format)
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 * A220856 A035599 A222556

Adjacent sequences:  A107480 A107481 A107482 * A107484 A107485 A107486

KEYWORD

nonn,base

AUTHOR

John W. Layman, Jun 09 2005

STATUS

approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)