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 4^{th} and last
nonzero 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
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