A099409 Numbers k such that 2*R_k + 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 3, 9, 15, 28, 64, 1168, 1695, 2362, 116620, 336405

Offset: 1

Author

Robert G. Wilson v, Oct 14 2004

Keywords

• nonn

Comments

Also numbers k such that (2*10^k + 43)/9 is prime.

a(11) > 50000. - Robert Price, Oct 27 2014

Links

• Makoto Kamada, Prime numbers of the form 22...227.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A056677, A093167.

Programs

Magma

[n: n in [0..1000] | IsPrime( 2*(10^n - 1) div 9 + 5)]; // Vincenzo Librandi, Oct 28 2014

Mathematica

Do[ If[ PrimeQ[ 2(10^n - 1)/9 + 5], Print[n]], {n, 0, 5000}]

Formula

a(n) = A056677(n-1) + 1.

Extensions

Added a(1)=0, adapted Mathematica program, Vincenzo Librandi, Oct 28 2014

a(11)-a(12) from Kamada data by Tyler Busby, May 03 2024