A056683 Numbers k such that 40*R_k + 9 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

2, 4, 5, 47, 107, 244, 1043, 20207, 52739, 89188

Offset: 1

Author

Robert G. Wilson v, Aug 10 2000

Keywords

• hard
• nonn

Comments

Also numbers k such that (4*10^(k+1) + 41)/9 is prime.

a(11) > 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, A099414.

Programs

Magma

[n: n in [0..300] | IsPrime((4*10^(n+1)+41)div 9)]; Vincenzo Librandi, Nov 10 2014

Mathematica

Do[ If[ PrimeQ[40*(10^n - 1)/9 + 9], Print[n]], {n, 5000}]

Formula

a(n) = A099414(n+1) - 1. - Robert Price, Nov 09 2014

Extensions

a(8)-a(10) derived from A099414 by Robert Price, Nov 09 2014