A056698 Numbers k such that 10^k + 3*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 15, 41, 83, 95, 341, 551, 669, 989, 1223, 6923, 103703

Offset: 1

Author

Robert G. Wilson v, Aug 10 2000

Keywords

• nonn
• hard
• more

Comments

Also numbers k such that (4*10^k-1)/3 is prime.

a(13) > 850000 (from Kamada data). - Robert Price, Oct 19 2014

Links

• Makoto Kamada, Prime numbers of the form 133...33.
• Index entries for primes involving repunits

Crossrefs

Cf. A002275, A093671, A097166, A259050.

Programs

Mathematica

Do[ If[ PrimeQ[ 10^n + 3*(10^n-1)/9], Print[n]], {n, 0, 30470}]

PARI

for(k=1,1500,if(ispseudoprime(4*(10^k-1)/3+1),print1(k, ", "))) \\ Hugo Pfoertner, Jul 22 2020

Extensions

a(12) from Kamada data by Robert Price, Oct 19 2014