%I #11 Jul 08 2021 01:23:58

%S 6,8,894,1524,3036,21156

%N Numbers k such that 2*R_k + 3*10^k + 1 is prime, where R_k = 11...11 is the repunit (A002275) of length k.

%C Also, numbers k such that (29*10^k + 7)/9 is prime.

%C Terms from Kamada data.

%C a(7) > 10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/abbba.htm">Near-repdigit numbers of the form ABB...BBA</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/32223.htm#prime">Prime numbers of the form 322...223</a>.

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

%e For k=6, 2*R_6 + 3*10^k + 1 = 222222 + 3000000 + 1 = 3222223 which is prime.

%t Select[Range[0, 100000], PrimeQ[(29*10^#+7)/9] &]

%Y Cf. A002275.

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Jun 18 2015