A229364 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).

1, 3, 5, 7, 9, 11, 23, 41, 53, 61, 73, 81, 93, 101, 223, 401, 523, 601, 723, 801, 923, 1001, 2223, 4001, 5223, 6001, 7223, 8001, 9223, 10001, 22223, 40001, 52223, 60001, 72223, 80001, 92223, 100001, 222223, 400001, 522223, 600001, 722223, 800001, 922223

Offset: 1

Author

Reinhard Zumkeller, Sep 21 2013

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,0,0,10,0,-10).

Crossrefs

Cf. A030284, A030283, A229363, A005408.

Programs

Haskell

import Data.List (intersect)
a229364 n = a229364_list !! (n-1)
a229364_list = f "" [1, 3 ..] where
   f xs (o:os) = if null $ intersect xs ys then o : f ys os else f xs os
                 where ys = show o

Formula

From Chai Wah Wu, Oct 21 2024: (Start)

a(n) = a(n-2) + 10*a(n-8) - 10*a(n-10) for n > 15.

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)