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%I #11 Jan 09 2024 12:17:02
%S 2,20,100,122,2222,20000,100000,122222,2222222,20000000,100000000,
%T 122222222,2222222222,20000000000,100000000000,122222222222,
%U 2222222222222,20000000000000,100000000000000,122222222222222
%N 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 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 From the above would follow that sequence has a rational g.f.
%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
%e 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 Cf. A054464.
%K nonn,base
%O 1,1
%A _John W. Layman_, Jun 09 2005
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