A167668 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.

0, 42, 6008, 22738

Offset

1,2

Comments

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

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.

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

Links

Table of n, a(n) for n=1..4.

Example

Example : 22738 is in the sequence, because
The digit 1 doesn't appear in 22738^1
The digit 2 doesn't appear in 22738^2 = 517016644
The digit 3 doesn't appear in 22738^3 = 11755924451272
The digit 4 doesn't appear in 22738^4 = 267306210173022736
The digit 5 doesn't appear in 22738^5 = 6078008606914190971168
The digit 6 doesn't appear in 22738^6 = 138201759704014874302417984
The digit 7 doesn't appear in 22738^7 = 3142431612149890211888380120192

Crossrefs

Sequence in context: A101630 A273628 A005791 * A277665 A215837 A211908

Adjacent sequences: A167665 A167666 A167667 * A167669 A167670 A167671

Keyword

fini,nonn,base

Author

Jean-Marc Falcoz, Nov 08 2009

Status

approved