Thursday, September 10, 2015

Repunit and Repdigit Numbers

9/10/2015

Repunit and Repdigit Numbers



Repunit Numbers
9
1/9 =
0.
1  1  1  1  1…
OEIS sequence A000012.  The simplest sequence of positive numbers: the all 1's sequence. 
This digital sequence might also be described as powers of 1, beginning with 1^0, and written as single digit chunks.
OEIS sequence A002275.  This can also be read as all of the repunit numbers, or even all of the prime digit numbers.  Both of these sequences can be read in any order desired.
Repunit Numbers
0.
1  11  111  1111  11111 
or
Prime Repunit Numbers
0.
11  1111111111111111111  11111111111111111111111 

Three is the smallest Sequence Number
3
1/3 =
0.
3  33  333  3333  33333 
This sequence contains all possible concatenations using only the digit “3”.  At the same time all of the possible concatenations are arranged in any order desired.  Example:
0.0
3333  3  33333333  33  3333333333333 



Similar numbers can be used to produce the repdigit numbers that use the digits 2 through 9.  Below I show you a way to produce the prime repdigit numbers.
Prime Repdigit Numbers
All of the Prime Repdigit Numbers can be generated by the sum of the results of four sequence numbers:
5, 28, 107,682, and 25,123,287,420
1/5 + 1/28 + 1/107682 + 1/25123287420 =
0.
2  3  5  7  2  3  5  7 
Written in single digit strings.
Accurate to the 4th and last non-zero term.
This sequence can also represent all of the single digit primes, as the first four primes, or as the first four Mersenne Exponents.




David

No comments:

Post a Comment