Repunit Prime/Sequence/Indices

Sequence of 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:

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

This sequence is A004023 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


According to On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008), only up to $R_{86 \, 453}$ are known to be prime.

The rest are only probably prime.


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): $1,111,111,111,111,111,111$
  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): repunit
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): repunit
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