A229145 -id:A229145 - cp's OEIS frontend

A348170 Numbers k such that (35^k - 1)/34 is prime.

313, 1297, 568453

Offset: 1

Paul Bourdelais, Oct 04 2021

These are the repunit primes in base 35.

			313 is a term since (35^313 - 1)/34 is a prime. It has 482 digits in base 10.

Paul Bourdelais, A Generalized Repunit Conjecture

Cf. A309533, A309532, A237052, A229145, A057191, A057182, A057175.

Cf. A218738.

Do[ If[ PrimeQ[ (35^n-1)/34], Print[n]], {n, 0, 600000}]

PARI
```
is(n)=isprime((35^n-1)/34)
```

A350036 Numbers k such that (81^k + 1)/82 is prime.

Original entry on oeis.org

3, 5, 701, 829, 1031, 1033, 7229, 19463, 370421

Offset: 1

Paul Bourdelais, Dec 09 2021

These are the Repunits in base -81. Since 81=3^4, factors will be of the form p=8nk+1. (Negative) bases that are powers of small numbers appear to have a higher frequency of primes than Repunits in other bases. The best linear fit for this base is currently 0.29918 which is much lower (better) than the conjectured 0.56145948 (see link to conjecture).

			3 is a term since (81^3 + 1)/82 = 6481 is a prime.

Paul Bourdelais, A Generalized Repunit Conjecture

Cf. A309533, A309532, A237052, A229145, A057191, A057182, A057175.

Do[ If[ PrimeQ[ (81^n+1)/82], Print[n]], {n, 0, 1000000}]

PARI
```
is(n)=isprime((81^n+1)/82)
```

cp's OEIS Frontend

A348170 Numbers k such that (35^k - 1)/34 is prime.

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