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Numbers k such that 2*10^k + 8*R_k - 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
1

%I #20 Jan 04 2021 04:49:23

%S 1,2,7,28,73,295,494,598,2600,3730,7549,15865

%N Numbers k such that 2*10^k + 8*R_k - 5 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (26*10^k-53)/9 is prime.

%C a(13) > 10^5. - _Robert Price_, Apr 18 2014

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/28883.htm#prime">Prime numbers of the form 288...883</a>.

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

%F a(n) = A101970(n) + 1.

%t Do[ If[ PrimeQ[(26*10^k - 53)/9], Print[k]], {k, 1, 10000}]

%Y Cf. A002275, A101970.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 17 2004

%E Addition of a(12) from Kamada data by _Robert Price_, Dec 13 2010

%E 0 removed by _Georg Fischer_, Jan 03 2021