A099414 Numbers k such that 4*R_k + 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 3, 5, 6, 48, 108, 245, 1044, 20208, 52740, 89189, 130080, 183657, 197061, 348453

Offset: 1

Author

Robert G. Wilson v, Oct 14 2004

Keywords

• nonn
• more

Comments

Also numbers k such that (4*10^k + 41)/9 is prime.

a(12) > 10^5. - Robert Price, Nov 09 2014

Links

• Makoto Kamada, Prime numbers of the form 44...449.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A056683.

Programs

Magma

[n: n in [0..300] | IsPrime((4*10^n+41) div 9)]; // Vincenzo Librandi Nov 10 2014

Mathematica

Do[ If[ PrimeQ[ 4(10^n - 1)/9 + 5], Print[n]], {n, 5000}]

Formula

a(n) = A056683(n-1) + 1.

Extensions

a(9)-a(11) from Robert Price, Nov 09 2014

a(12)-a(15) from Kamada data by Tyler Busby, Apr 29 2024