A160015 a(n) = smallest positive number having no digits in common with n and greater than any earlier term.

2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 23, 30, 40, 50, 60, 70, 80, 90, 200, 311, 330, 331, 400, 500, 600, 700, 800, 900, 1000, 1111, 2000, 4000, 4001, 5000, 6000, 7000, 8000, 9000, 10000, 11111, 20000, 30000, 50000, 50001, 60000, 70000, 80000, 90000, 100000

Offset

1,1

Comments

Sequence is finite: the last index is <= 123456788. a(123456789) cannot exist, since a number cannot contain all 0's. - Dmitry Kamenetsky, Jun 16 2009

What is the last term? - Robert G. Wilson v, May 27 2009

The last index is indeed n = 123456788 and the last a(n) = 9(10^12362882) + 999. - Robert G. Wilson v, Jun 07 2010

Links

Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000

Dmitry Kamenetsky, Java program

Example

a(10)=22 because 22 is the smallest number > a(9) that doesn't contain 0 or 1.

Mathematica

f[Infinity, _] = Infinity; f[_, Range[0, 9] | Range[1, 9]] = Infinity; f[x_Integer, z_Integer] := f[IntegerDigits[1 + x], Union@IntegerDigits@z]; f[x_List, z_List] := Module[{n = Length@x, k = Flatten@ Position[x, Alternatives @@ z, 1, 1], low = Min@ Complement[ Range[0, 9], z]}, If[k == {}, FromDigits@x, k = First@k; f[10^(n - k) + FromDigits@ Flatten@ {Take[x, k], ConstantArray[low, n - k]} // IntegerDigits, z]]]; a[0] = 1; a[n_] := f[a[n - 1], n]; Array[a, 100] (* the function f(x, z) is from Bobby R. Treat (drbob(at)bigfoot.com) *) (* or *) k = 1; NestList[(k++; f[ #, k]) &, 2, 99] (* Robert G. Wilson v, Jun 07 2010 *)

Crossrefs

Cf. A096779.

Sequence in context: A099469 A358097 A039112 * A276392 A132271 A116069

Adjacent sequences: A160012 A160013 A160014 * A160016 A160017 A160018

Keyword

nonn,base,fini

Author

Rodolfo Kurchan, Apr 29 2009

Extensions

a(43)-a(90) from Dmitry Kamenetsky, May 03 2009

Incorrect b-file and Mathematica program deleted by N. J. A. Sloane, Jun 13 2009

Status

approved