Repunit Prime/Sequence

Sequence of Repunit Primes

The sequence of repunit primes (base $10$) begins:

$11, 1 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111, 11 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111 \, 111, \ldots$

This sequence is A004022 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Repunit Primes by Indices

Expressing a repunit prime of $n$ digits by $R_n$, the complete sequence of known repunit primes (base $10$) can be expressed as:

$R_2, R_{19}, R_{23}, R_{317}, R_{1031}, R_{49 \, 081}, R_{86 \, 453}, R_{109 \, 297}, R_{270 \, 343}, R_{5 \, 794 \, 777}, R_{8 \, 177 \, 207}$


Linguistic Note

The derivation of the term repunit is clear: it comes from repeated unit.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,111,111,111,111,111,111$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,111,111,111,111,111,111$
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