A102945 Numbers k such that 10^k + 8*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

1, 3, 12, 267, 843, 6300, 37992, 54117, 121242, 121621

Offset: 1

Author

Robert G. Wilson v, Dec 16 2004

Keywords

• more
• nonn

Comments

Also numbers k such that (17*10^k + 1)/9 is prime.

No more terms below 133000. - Serge Batalov, May 15 2010

a(11) > 2*10^5. - Robert Price, Nov 16 2014

Links

• Makoto Kamada, Prime numbers of the form 188...889.
• Index entries for primes involving repunits.

Crossrefs

Cf. A002275, A102031.

Programs

Magma

[n: n in [0..300] | IsPrime((17*10^n+1) div 9)]; // Vincenzo Librandi, Nov 17 2014

Maple

A102945:=n->`if`(isprime((17*10^n+1)/9), n, NULL): seq(A102945(n), n=1..10^3); # Wesley Ivan Hurt, Nov 16 2014

Mathematica

Do[ If[ PrimeQ[(17*10^n + 1)/9], Print[n]], {n, 0, 10000}]
Select[Range[1000], PrimeQ[(17 10^# + 1) / 9] &] (* Vincenzo Librandi, Nov 17 2014 *)

Formula

a(n) = A102031(n) + 1.

Extensions

More PRP terms a(7)-a(10). Sieved with srsieve and tested with Prime95 by Serge Batalov, May 15 2010