Republic of Mathematics blog

Posts Tagged ‘powers of 2

How many zeros are there in 2^n?

Posted by: Gary Ernest Davis on: April 23, 2011

An old problem asks if is the highest power of whose base representation: , does not contain the digit . For instance, the next powers of do indeed contain the digit : x How many zeros? Instead of asking the existential question “Is there a zero in the base representation of for ?” we can […]

Some curly questions on the base 3 digits of powers of 2

Posted by: Gary Ernest Davis on: December 6, 2010

Representing positive integers base 3 Positive whole numbers can easily be written in base 3, there where we allow the digits 0, 1, 2 For example: which we write as , where the notation picks out the digits and puts a subscript “3” to remind us that these digits need to be multiplied by appropriate […]