%I #8 Oct 21 2024 14:27:02
%S 1,3,5,7,9,11,23,41,53,61,73,81,93,101,223,401,523,601,723,801,923,
%T 1001,2223,4001,5223,6001,7223,8001,9223,10001,22223,40001,52223,
%U 60001,72223,80001,92223,100001,222223,400001,522223,600001,722223,800001,922223
%N a(1) = 1; for n > 1: a(n) = smallest odd number greater than a(n-1) which does not use any digit used by a(n-1).
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,0,0,10,0,-10).
%F From _Chai Wah Wu_, Oct 21 2024: (Start)
%F a(n) = a(n-2) + 10*a(n-8) - 10*a(n-10) for n > 15.
%F G.f.: x*(-10*x^14 - 20*x^13 - 20*x^12 - 20*x^11 - 20*x^10 - 10*x^9 + 20*x^8 + 30*x^7 + 14*x^6 + 4*x^5 + 4*x^4 + 4*x^3 + 4*x^2 + 3*x + 1)/((x - 1)*(x + 1)*(10*x^8 - 1)). (End)
%o (Haskell)
%o import Data.List (intersect)
%o a229364 n = a229364_list !! (n-1)
%o a229364_list = f "" [1, 3 ..] where
%o f xs (o:os) = if null $ intersect xs ys then o : f ys os else f xs os
%o where ys = show o
%Y Cf. A030284, A030283, A229363, A005408.
%K nonn,base,easy
%O 1,2
%A _Reinhard Zumkeller_, Sep 21 2013