A099413 Numbers k such that 4*R_k + 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 1, 2, 4, 10, 20, 26, 722, 1310, 3170, 28934, 66284, 67796, 231254, 338476

Offset: 1

Author

Robert G. Wilson v, Oct 14 2004

Keywords

• nonn
• hard
• more

Comments

Also numbers k such that (4*10^k + 23)/9 is prime.

a(14) > 10^5. - Robert Price, Nov 26 2014

Links

• Makoto Kamada, Prime numbers of the form 44...447.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A056682.

Programs

Mathematica

Do[ If[ PrimeQ[ 4(10^n - 1)/9 + 3], Print[n]], {n, 5000}]

Formula

a(n) = A056682(n-1) + 1. - Robert Price, Nov 26 2014

Extensions

a(11)-a(13) from Robert Price, Nov 26 2014

a(14)-a(15) from Kamada data by Tyler Busby, May 03 2024