A056725 - OEIS

%I #41 Jul 19 2021 04:32:04

%S 1,3,7,19,29,37,93,935,8415,9631,11143,41475,41917,48051,107663,

%T 212903,223871,260253,364521,383643,1009567,1762063

%N Numbers k such that 9*10^k - 1 is prime.

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

%C 1009567 is also a member of this sequence, but its position is presently undetermined: 9 * 10^1009567 - 1 is prime. - _Predrag Kurtovic_, Sep 19 2016

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/8/89999.htm#prime">Prime numbers of the form 899...999</a>.

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

%t Do[ If[ PrimeQ[ 8*10^n + (10^n-1)], Print[n]], {n, 1, 6750, 2}]

%o (PARI) is(n)=isprime(9*10^n-1) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A003307, A002235, A046865, A079906, A046866, A001771, A005541, A046867, A079907.

%K hard,nonn,more

%O 1,2

%A _Robert G. Wilson v_, Aug 11 2000

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

%E a(16)-a(20) from Kamada data by _Robert Price_, Oct 19 2014

%E a(21) from Kamada data by _Robert Price_, Mar 10 2019

%E a(22) from Kamada data by _Mohammed Yaseen_, Jul 18 2021