%I #38 Jul 03 2023 00:58:36

%S 1,2,3,4,14,15,23,28,54,100,272,373,403,568,639,842,969,1255,1259,

%T 3047,4838,6389,12755,15142,34943,37652,38108,38686,39384,43393,47280,

%U 55030,161192,226479

%N Numbers k such that 7*10^k - 9 is prime.

%C Also numbers k such that 6*10^k + 9*R_k - 8 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C a(35) > 3*10^5. - _Robert Price_, Jul 02 2023

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/6/69991.htm#prime">Prime numbers of the form 699...991</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A101541(n) + 1.

%t Do[ If[ PrimeQ[7*10^n - 9], Print[n]], {n, 0, 10000}]

%t Select[Range[100000], PrimeQ[(7 10^# - 9)] &] (* _Vincenzo Librandi_, Oct 15 2015 *)

%o (Magma) [n: n in [1..500] | IsPrime(7*10^n-9)]; // _Vincenzo Librandi_, Oct 15 2015

%o (PARI) isok(n) = isprime(7*10^n-9 ); \\ _Michel Marcus_, Oct 15 2015

%Y Cf. A002275, A101541.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 18 2005

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

%E Addition of a(25)-a(32) from Kamada data by _Robert Price_, Dec 13 2010

%E a(33) from _Robert Price_, Oct 14 2015

%E a(34) from _Robert Price_, Jul 02 2023