Repunit Prime/Sequence
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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): $1,111,111,111,111,111,111$