A030283 - OEIS

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

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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.