A160015 - OEIS

%I #18 Aug 02 2015 17:15:34

%S 2,3,4,5,6,7,8,9,10,22,23,30,40,50,60,70,80,90,200,311,330,331,400,

%T 500,600,700,800,900,1000,1111,2000,4000,4001,5000,6000,7000,8000,

%U 9000,10000,11111,20000,30000,50000,50001,60000,70000,80000,90000,100000

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

%C 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

%C What is the last term? - _Robert G. Wilson v_, May 27 2009

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

%H Dmitry Kamenetsky, <a href="/A160015/b160015.txt">Table of n, a(n) for n = 1..10000</a>

%H Dmitry Kamenetsky, <a href="/A160015/a160015.java">Java program</a>

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

%t 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 *)

%Y Cf. A096779.

%K nonn,base,fini

%O 1,1

%A _Rodolfo Kurchan_, Apr 29 2009

%E a(43)-a(90) from _Dmitry Kamenetsky_, May 03 2009

%E Incorrect b-file and Mathematica program deleted by _N. J. A. Sloane_, Jun 13 2009