A056694 Numbers k such that 80*R_k + 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 2, 4, 7, 8, 14, 50, 70, 76, 223, 295, 314, 2089, 2905, 3394, 3881, 5113, 6055, 7253, 7994, 18172, 18970, 35005, 69673

Offset: 1

Author

Robert G. Wilson v, Aug 10 2000

Keywords

• hard
• nonn

Comments

Also numbers k such that (8*10^(k+1)-53)/9 is prime.

a(26) > 10^5. - Robert Price, Oct 31 2014

Links

• Makoto Kamada, Prime numbers of the form 88...883.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A093166, A099422.

Programs

Magma

[n: n in [0..500] | IsPrime((8*10^(n+1)-53) div 9)]; // Vincenzo Librandi, Nov 01 2014

Mathematica

Do[ If[ PrimeQ[80*(10^n - 1)/9 + 3], Print[n]], {n, 0, 5000}]

Formula

a(n) = A099422(n) - 1. [adapted by Georg Fischer, Jan 04 2021]

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(22)-a(25) from Robert Price, Oct 31 2014