A099422 Numbers k such that 8*R_k - 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 2, 3, 5, 8, 9, 15, 51, 71, 77, 224, 296, 315, 2090, 2906, 3395, 3882, 5114, 6056, 7254, 7995, 18173, 18971, 35006, 69674, 175428, 253313

Offset: 1

Author

Robert G. Wilson v, Oct 14 2004

Keywords

• nonn

Comments

Also numbers k >= 1 such that (8*10^k - 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, A056664, A056694, A093166.

Programs

Magma

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

Mathematica

Do[ If[ PrimeQ[ 8(10^n - 1)/9 - 5], Print[n]], {n, 1, 5000}]

Formula

a(n) = A056694(n) + 1.

Extensions

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

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

a(1)=0 removed by Georg Fischer, Jan 03 2021

a(26)-a(27) from Kamada data by Tyler Busby, Apr 16 2024