A167668 - OEIS

%I #2 Mar 31 2012 10:24:15

%S 0,42,6008,22738

%N Nonnegative integers n such that n^j doesn't contain the digit j (1<=j<=7) and n is not a multiple of a smaller member of the sequence.

%C If multiples could appear in the sequence, then 10^x * 22738 would also be in the sequence.

%C I've tested the integers up to 100000000. I believe 22738 is the greatest integer with this property, but I don't have a proof.

%C Similarly, I think there's no integer with the same property up to 8, but again, I have no proof of this.

%e Example : 22738 is in the sequence, because

%e The digit 1 doesn't appear in 22738^1

%e The digit 2 doesn't appear in 22738^2 = 517016644

%e The digit 3 doesn't appear in 22738^3 = 11755924451272

%e The digit 4 doesn't appear in 22738^4 = 267306210173022736

%e The digit 5 doesn't appear in 22738^5 = 6078008606914190971168

%e The digit 6 doesn't appear in 22738^6 = 138201759704014874302417984

%e The digit 7 doesn't appear in 22738^7 = 3142431612149890211888380120192

%K fini,nonn,base

%O 1,2

%A _Jean-Marc Falcoz_, Nov 08 2009