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

0,3

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).

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A358097.

Cf. A068860, A068861, A229363, A229364.

Sequence in context: A132271 A116069 A081511 * A276633 A298482 A301801

Adjacent sequences: A030280 A030281 A030282 * A030284 A030285 A030286

Keyword

nonn,base,easy,nice

Author

Patrick De Geest

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

Status

approved