A229363 -id:A229363 - cp's OEIS frontend

A030283 a(0) = 0; for n>0, a(n) is the smallest number greater than a(n-1) which does not use any digit used by a(n-1).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 30, 41, 50, 61, 70, 81, 90, 111, 200, 311, 400, 511, 600, 711, 800, 911, 2000, 3111, 4000, 5111, 6000, 7111, 8000, 9111, 20000, 31111, 40000, 51111, 60000, 71111, 80000, 91111, 200000, 311111, 400000, 511111, 600000

Offset: 0

Patrick De Geest

The sequence is infinite.

Reinhard Zumkeller, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,0,0,10,0,-10).

Cf. A358097.

Cf. A068860, A068861, A229363, A229364.

a030283 n = a030283_list !! n
a030283_list = 0 : f 1 9 0 where
   f u v w = w' : f u' v' w' where
     w' = until (> w) ((+ v) . (* 10)) u
     (u',v') = h u v
     h 1 0 = (2,2); h 9 0 = (1,1); h 9 1 = (2,0); h 9 9 = (1,0)
     h u 2 = (u+1,0); h u v = (u+1,1-v)
-- Reinhard Zumkeller, May 03 2012

a = {0}; For[n = 1, n < 1000000, n++, If[Length[Intersection[IntegerDigits[n], IntegerDigits[a[[ -1]]]]] == 0, AppendTo[a, n]]]; a (* Stefan Steinerberger, May 30 2007 *)

a(n) = a(n-2) + 10*a(n-8) - 10*a(n-10) for n > 29. - Nicolas Bělohoubek, Jul 01 2024

Edited by N. J. A. Sloane at the suggestion of Rick L. Shepherd, Sep 27 2007

Definition clarified by Harvey P. Dale, Oct 19 2012

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).

Original entry on oeis.org

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

Reinhard Zumkeller, Sep 21 2013

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

Cf. A030284, A030283, A229363, A005408.

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

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)

cp's OEIS Frontend

A030283 a(0) = 0; for n>0, a(n) is the smallest number greater than a(n-1) which does not use any digit used by a(n-1).

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