# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a107483 Showing 1-1 of 1 %I A107483 #11 Jan 09 2024 12:17:02 %S A107483 2,20,100,122,2222,20000,100000,122222,2222222,20000000,100000000, %T A107483 122222222,2222222222,20000000000,100000000000,122222222222, %U A107483 2222222222222,20000000000000,100000000000000,122222222222222 %N 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). %F A107483 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. %F A107483 From the above would follow that sequence has a rational g.f. %F A107483 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 %e A107483 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. %Y A107483 Cf. A054464. %K A107483 nonn,base %O A107483 1,1 %A A107483 _John W. Layman_, Jun 09 2005 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE