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

Author

Patrick De Geest

Keywords

• nonn
• base
• easy
• nice

Comments

The sequence is infinite.

Links

• 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).

Crossrefs

Cf. A358097.

Cf. A068860, A068861, A229363, A229364.

Programs

Haskell

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

Mathematica

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 *)

Formula

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

Extensions

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